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Article

The Study of Historical Progression in the Distribution of Urban Commercial Space Locations—Example of Paris

by
Jingyuan Zhang
1,
Jusheng Song
1,* and
Zouyang Fan
2
1
Urban Planning Department, Faculty of Architecture, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
2
Economics and Management Department, Xiamen University of Technology, Xiamen 361005, China
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(19), 14499; https://doi.org/10.3390/su151914499
Submission received: 13 September 2023 / Revised: 28 September 2023 / Accepted: 3 October 2023 / Published: 5 October 2023
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Abstract

:
Commercial space locations are a long-term investment for developers, and they are crucial for sustainable profitability. The distribution of commercial spaces in Paris has undergone a constant evolutionary process over the past few centuries, influenced by various socioeconomic factors. This study investigates the evolution of commercial space locations in Paris over three historical stages—1690, 1860, and 2023, using Space Syntax and Cluster Analysis. By examining the historical progression of Parisian commercial spaces from an urban planning perspective, this article aims to provide insights for urban developers to strategically plan for commercial spaces. The first part of the study is an analysis of the centrality and accessibility of commercial space locations within the urban street network using Space Syntax. Next, Cluster Analysis is employed to further examine the distribution patterns of commercial spaces with high centrality. By comparing the results from three different historical stages, the study reveals two major patterns. One is a full-scale optimization of commercial space centrality within the historical core of Paris. Another one is the fission and consolidation of commercial spaces into multi-centric clusters and a geographical dispersal from central Paris. Finally, a multi-disciplinary discussion is conducted to decode the socioeconomic motivations behind these patterns and provide guidance for future commercial planning.

1. Introduction

During a time of mass production when urban commercial spaces distribute homogeneous commercial products, the factor that distinguishes the competitiveness of commercial spaces is their locations within the city network [1,2,3]. Applebaum, W. (1968) [4] states that due to inadequate customer attention and uneven distribution of purchasing power, the locations of commercial spaces significantly impact sales. Furthermore, at a time when urban spaces are becoming scarce, the locations of large-scale commercial spaces are considered as a long-term investment. Altering locations entails substantial costs, including the acquisition of new land plots and the construction of new buildings [5]. Therefore, strategic planning for commercial space locations is crucial for sustainable profitability [5,6,7].
Commercial space locations originated from an economic theoretical background, which was phrased as retail location theory developed in the early 20th century [8]. According to the Central Place Theory by Christaller, centrality is the key factor in selecting commercial locations, as it provides the highest accessibility to potential customers within the trading area, ensuring maximum foot traffic [9]. Haig’s Bid-Rent theory (1927) validates the centrality concept from a land market perspective, highlighting that due to the speculative nature of urban land resources, the most accessible and central locations will always be bid to commercial sectors [10]. Last but not least, the principle of minimum differentiation developed by H. Hotelling (1929) suggests that clustering is the best model for choosing locations for multiple vendors selling the same type of product and competing for the same group of potential customers in an area [11]. These theories, grounded in economic principles, establish the qualitative attributes of commercial space locations, which are centrality, accessibility, and clustering.
Scholars in the field of urban planning, on the other hand, have conducted quantitative research on commercial space locations, which have testified to the attributes outlined by economic theories. Their studies have confirmed that, at the scale of streets and neighborhoods, a strong positive correlation between centrality, accessibility, clustering, and commercial activities can be observed [12,13]. Furthermore, research conducted at the city scale has revealed a consistent pattern of commercial space decentralization. For instance, Dong (2013) used a location choice simulation model to simulate the decision-making behavior. The study demonstrated that commercial spaces decentralized from the central city of the metropolitan area of Portland, US [14]. In Portugal, Europe, Saraiva et al. (2017) investigated the patterns found in the geospatial distribution of commercial spaces in four cities in Portugal. The study arrived at a similar conclusion, where the city center and suburban areas exhibited different distribution models [15]. Although the research findings are highly rigorous and concrete, they have thus far remained focused on analyzing the existing state of affairs. The underlying determinants of commercial site selection patterns are yet to be explored.
In fact, there are scholars who stated that commercial spaces and urban forms are co-evolving entities, and they impact each other [15,16]. The locations of commercial spaces are fundamentally influenced by the socioeconomic context of a city [17]. Investigating the evolution patterns of commercial space locations under changing urban contexts allows us to decode the social determinants of commercial space locations. Therefore, a study from the perspective of historical progression is necessary.
Paris emerged as a suitable site for three reasons. Firstly, as a city that has existed since the Middle Ages, Paris provides us with the opportunity to observe urban fabric across various historical periods and social contexts. For instance, the medieval city fabric in the heart of Paris coexists with several individual public squares built during the 15th and 16th centuries, while the majority of the cityscape was constructed during the 19th and 20th centuries. Secondly, as the world capital of shopping, Paris undoubtedly nurtured successful commercial space systems. According to the latest data, the percentage of commercial activities as a proportion of the city’s GDP output is as follows: Paris 80.6% [18], Luxembourg 79.3% [19], Shanghai 74.1% [20]. These figures indicate that commercial spaces in Paris effectively channel economic activities. Lastly, during the course of urban development, Parisian commercial spaces have consistently undergone self-renewal, primarily within the historical city center, according to our research findings. This provides valuable insights for municipalities grappling with suburbanization and the deterioration of their central districts.
Common tools for examining commercial land use are GIS and Space Syntax. While GIS can integrate diverse societal datasets to analyze correlations among factors, its granularity is relatively coarse [21]. In the study by M. Fragkias et al., urban morphology is represented as a grid with uniform dimensions of 30 × 30 m, which broadly depicts human circulation in the city [22]. However, Space Syntax provides a more realistic depiction of human movement in cities, making it particularly suited for assessing the attractiveness of commercial spaces [23]. Space Syntax metrics directly align with fundamental theories of commercial site selection, including centrality and accessibility [24,25,26,27]. In addition to centrality, clustering is another key attribute of commercial space distribution [11], leading us to incorporate spatial clustering analysis following Space Syntax analysis of the urban street network. Studies have shown that spatial clustering algorithms can scientifically classify groups of clusters based on the geographical proximity among a large number of unsorted urban elements [28,29].
In summary, validated by a range of economic scholars, strategic planning of commercial space locations is crucial because it can lead to sustainable profitability for commercial firms. Scholars in the field of urban planning have conducted in-depth quantitative analysis of the current distribution of commercial space locations in particular cities. However, this field still presents two research gaps. Firstly, the relationship between commercial space layout and socioeconomic factors has yet to be explored. Secondly, existing research tools have not yet demonstrated a targeted approach to commercial activities or site selection.
Based on the existing research framework for commercial site selection, this study aims to achieve four novel objectives. Firstly, it seeks to identify patterns in the historical progression of the distribution of commercial spaces in Paris during different historical periods. Secondly, the article aims to elucidate the underlying determinants of the progressive patterns by conducting interdisciplinary discussions that integrate socioeconomic knowledge. Thirdly, a hybrid research methodology that combines Space Syntax and Clustering Analysis is employed to specifically analyze the centrality, accessibility, and clustering patterns of commercial space locations. Lastly, this study aspires to provide insights for sustainable commercial planning to urban decision-makers based on a historical progression study.
The following article is divided into four parts. First, following the introduction, Section 2 clarifies the source of the materials of the study and briefly summarizes the urban configuration of Paris during the investigated time periods. Additionally, in Section 2, the rationale of the research methodologies are explained. Section 3 presents the visualized results of the Space Syntax and Clustering Analysis of commercial space locations from different time periods in Paris. In Section 4, an interdisciplinary discussion is conducted to rationalize the pattern exhibited from the analysis results, and explain how socioeconomic context have influenced the progression. Finally, in Section 5, we conclude the study by consolidating insights from the results and formulate universal guidance for decision makers from other cities.

2. Materials and Methods

2.1. Materials: Commercial Spaces in Paris 1690, 1860 and 2023

The commercial spaces analyzed in our study are those with an independent site area of no less than 1000 m2. Only commercial spaces at a certain scale can effectively aggregate commercial activities, which constitute an important part of urban public life [30]. Furthermore, commercial spaces of a certain scale are facing a competitive environment for location choosing compared to small shops [31], making them a suitable subject for our study.
In our investigation of Paris, the city’s urban morphology has evolved significantly during three remarkable time periods: the Monarchy in the 17th century, Haussmanization in the mid-19th century, and post-industrialization from the late 20th century to the present day. The historical research of the commercial space locations is based on the commercial spaces and city configuration from these three time periods.
Since medieval times, Paris’s dense urban layout has facilitated merchant trading [32]. By the 17th century, market halls and squares further solidified Paris as a trading hub, often commissioned by French Monarchs like Henry IV and Louis XIV to boost the economy and celebrate Monarchy authority. This resulted in a medieval city fabric adorned by grand commercial spaces [33]. During Paris’s industrialization from 18th to 19th century, manufacturing shifted from domestic to factory-based [34]. Commissioned by Baron Haussmann, new boulevards improved accessibility in the city center, while land speculation in the suburbs also enriched commercial opportunities [35], resulting in an expansion of commercial zones and an improved urban infrastructure network. In the mid-20th century, Paris transitioned to post-industrialism, witnessing a surge in commercial spaces specializing in retail sales of mass-produced products [36]. Location became the predominant factor influencing profitability. In summary, as a quintessential European city, Paris evolved via numerous urban metamorphoses, consistently revitalizing its commercial space system in the process. Thus, the study of the evolution of commercial spaces in Paris carries substantial research significance.
The historically archived maps from 1690 to 1860 were digitally accessed from Wikipedia Commons. 1690 map was drawn by Johannes de Ram (Appendix A, Figure A1), and the 1860 map was drawn by Andriveau Goujon (Appendix A, Figure A2). Due to the limitation of the map drawing technique in the 17th century, Johannes de Ram’s 1690 map was the most legible map that realistically represented the geography of Paris in the 17th century. The 1860 map was drawn during the mid-way point of Haussmann’s administration of Paris from the 1850s to the 1870s. The 1860 map was more objective in depicting the city during the course of the 19th century because the construction of Haussmann’s proposed construction continued into the 20th century [37]. The map of Paris in 2023 is accessible from OpenStreetMap. The street network was obtained using the software QGIS3 as poly-lines. Historical commercial spaces that exceed 1000 m2 in footprint are identified from historical maps, while commercial spaces from 2023 are directly inquired from the GIS platform.

2.2. Methods: Space Syntax

2.2.1. Urban Street Network Representation as “Axial Map”

Space syntax is an analysis method that calculates the connectivity of each element within a network of streets, developed by B.Hillier and his colleagues at UCL [38]. Street network configuration affects people’s movement patterns and their destinations, and therefore, it influences the social dynamism of spaces [39]. Space syntax analyzes the connectivity of streets to distinguish urban spaces that are easily accessible from those that are more segregated [40].
As input material for Space Syntax analysis, the axial map is a diagrammatic representation of urban street networks that focuses on pedestrian movement and the connectivity of streets [41]. The axial map is constructed based on the concept of “axial lines”, which is an abstraction of observers’ optimal movement through urban spaces. Axial lines represent the most straightforward route between destinations [42]. When all the spaces that people are free to travel, mostly streets, paths, and public squares, are represented as axial lines, we have an axial map ready for syntactical analysis [39].

2.2.2. Global Integration: Accessibility and Centrality of Commercial Spaces

One important measure of Space Syntax analysis is Global Integration, which indicates how well a street is connected to all other streets within a network of streets [43]. In other words, the Global Integration (GI) value indicates the centrality of urban streets [44]. The more central a street axis is within a network, the fewer turns other elements need to make to reach this street, and this street segment will have a higher GI value.
The steps to calculate Global Integration (GI) are referred to in Table 1.
The output of the process of GI calculation is a normalized measurement of the relative accessibility of an element within a network of streets. This allows for comparisons across urban street systems regardless of their sizes [38].
The Global Integration value derived from Space Syntax analysis indicates the hierarchy of streets [44] and is widely used to predict economic activity and suggest the dynamism of commercial spaces [45]. According to case studies conducted by B.Hillier in 1993, there’s a respectable correlation between commercial activities and the Global Integration value of streets in the studied areas [46]. The study demonstrates that urban development is a result of people’s natural movement, and greater accessibility within a network increases the likelihood of nurturing commercial activities. The function of a commercial center is to foster public activities, including trading, shopping, financial services, and so on. The location of such commercial spaces should optimize centrality in both geographical and topological terms in order to reach all potential customers [44].

2.3. Methods: K-Means Clustering Analysis

K-Means clustering algorithm is selected for further analysis of high-centrality streets identified using Space Syntax analysis. The input data for the clustering analysis will consist of coordinates from tessellated points within the urban street network at different historical times in Paris. The output of the clustering analysis will categorize streets spatially, and different high-centrality street network configurations are expected to yield distinct classification results.
K-Means Clustering analysis is used for planar spatial clustering, as studied by L. Kaufman and P. Rousseeuw [47]. A k-means clustering algorithm was first proposed by Lloyd [48,49,50]. The principle involves measuring similarity by calculating the distance between input point entities. The larger the distance, the lower the similarity, and ultimately, different categories within the sample are determined based on the similarity of positions [51]. The algorithm is not sensitive to the order of data input, meaning that even with different orders, the same result can be obtained. This property makes the algorithm highly stable and efficient in terms of clustering [52].
The specific working steps are:
  • The initial cluster center is set to randomly select k samples: a = a1, a2, …, an;
  • The distance to each cluster center xi was calculated, and the cluster center with the smallest distance was selected to partition the sample;
  • The distance from xi to each cluster center was calculated, and the cluster center with the smallest distance was selected to divide the sample;
  • The previous step calculates the category by calculating the weighted average sum and setting it as the new cluster center;
  • The distance from the sample to the cluster center was calculated iteratively (step 1), and the cluster center was updated (step 2), either if the threshold of the number of iterations has been reached or if the local minimum error has been obtained.
It is calculated by minimizing the sum of squared inter-group distances between the load curve and cluster centers, as shown in the following formula:
J = ∑ j = 1 k ∑ i = 1 , i ∈ j n L P i − C C j
In this formula, ‘LPi’ represents the vector of the ‘i’th load distribution, ‘CCj ’ represents the ‘j’th vector of the cluster center. The output of the algorithm is cluster centers. In each iteration of K-Means, the definition of cluster similarity is mainly based on the Euclidean formula to calculate the average Euclidean distance between the load distribution and cluster centers (Average Euclidean distance, AED). Therefore, each load curve is assigned to the cluster with the nearest center [53]. The calculation formula is the following:
A E D ( L P i , C C j ) = ∑ t = 1 T ( l p i ( t ) − c c j ( t ) ) 2 / T
The K-Means algorithm is essentially optimizing for the amount of clusters in which the input points can be classified. The number of clusters is represented as ‘k’ [54]. Elbow method is a commonly used method to determine cluster amount ‘k’, the calculation procedure is the following:
Given a sample of input data sample x 1 , x 2 , ⋯ , x m at m dimension, cluster analysis is performed using clustering algorithms. For the i th sample data, the cluster center of the i th class is denoted as m i . x is a data point that belongs to the i th class. SSE (Sum of Squared Errors) is the sum of squared errors between each point in each cluster and its corresponding cluster center, which varies with different amounts of clusters ‘k’ [55]. As the number of clusters increases, the rate of decrease of SSE stabilizes. When graphing the change in SSE for different values of ‘k’, the optimal number of clusters ‘k’ is where the change in the slope is the steepest, resembling the bend of an elbow. Data points are then assigned to the cluster with the highest similarity to C i j . After the assignment is completed, the average value of the data in each of the ‘k’ clusters are calculated, resulting in a new set of cluster centers. When SSE no longer converges, the final number of clusters is obtained using the following formula:
S S E = ∑ i = 1 k ∑ x ∈ C i d ( x , C i ) 2

2.4. Research Framework

In Section 3.1, the accessibility and centrality analysis of commercial space locations is conducted using Space Syntax. The analysis results are conveyed by superimposing the footprints of identified commercial spaces onto the Space Syntax output of the urban street network from the corresponding historical time. As shown in Figure 1, the first step of the Space Syntax analysis involves converting street networks from the maps into Axial Maps following the principle of Axial map drawing [42]. These axial maps are then imported into DepthmapX for Space Syntax analysis. The output would be a color-coded axial map, where the gradient of color, ranging from red to blue, indicates a range of GI values from high to low.
From the collected maps, extract the commercial spaces with footprints larger than 1000 m2 in area. On the historical maps of 1690 and 1860, the identified commercial spaces were primarily markets and public squares that were documented to be of public, commercial trading use [56]. Additionally, for the 2023 data, footprints of commercial and retail buildings were directly inquired from OpenStreetMap using QGIS3.16.2. Commercial spaces larger than 1000 m2 have a larger service radius, meaning that their customer flow is closely related to their location within the city.
Subsequently, Section 3.2 is a Cluster Analysis of the commercial spaces and highly integrated streets to further analyze the distribution pattern of commercial spaces. The result of Section 3.2 will be a map that superimposes the K-means clustering results of the highly integrated street and Euclidean distance clustering of the commercial spaces.
Using the K-Means clustering algorithm, the street network from three historical time periods with GI value above 0.8 will be classified into a number of clusters. Since the input data for spatial cluster analysis algorithms must be points, the highly integrated street elements are tessellated into points that mark equivalent lengths [28]. The coordinates of the tessellated points will be used as input for the K-Means clustering analysis. As an output of the clustering analysis, the overall configuration of highly integrated streets will be classified into clusters based on their geospatial locations. On the other hand, the Euclidean distance cluster analysis of commercial spaces is conducted by connecting line segments between any two commercial spaces if their Euclidean distances are closer than 1 KM, which is assumed to be the maximum distance one can travel between commercial spaces.
The research framework can be represented by the diagram below:

3. Results

In order to examine the historical progression pattern of commercial space locations in Paris, two consecutive quantitative analyses are conducted. First, in Section 3.1, the accessibility and centrality analysis of the locations of commercial spaces in Paris over three historical stages is performed using Space Syntax. Subsequently, Section 3.2 is the cluster analysis based on the results evaluated with centrality and accessibility from Section 3.1. This analysis aims to analyze the distribution pattern of high-centrality commercial spaces and their locations in relation to the street network. Both sections are structured chronologically, presenting test results and descriptions in the sequence of 1690, 1860, and 2023.

3.1. Accessibility and Centrality Analysis Using Space Syntax

The roads with the highest GI value are the north–south thoroughfare Rue Saint Martin-Rue Saint Jacques (①, Figure 2), along with a segment of Rue Saint-Denis (②, Figure 2) on the right bank of Paris. Along Rue Saint Martin-Saint Jacques, the street segment with a GI value above 0.9 extends for 6 km, covering almost the entire length of the street. The secondary streets connecting the two central roads are also highly integrated, primarily concentrated around the Les Halles area ③. While based on a strong north–south axis, there are a few streets running in the east–west direction with high GI values, including Rue Saint-Honoré (④, Figure 2), Rue Saint-Antoine (⑤, Figure 2) and Quay de la Mégisserie (⑥, Figure 2) along River Seine. However, the highly integrated street segments do not exceed 1.7 km in length.
As a result, the long and narrow quarters along the north–south axis of Paris exhibit the highest centrality and greatest potential for generating commercial activities. However, only about half of the commercial spaces are located near the central north–south axis and are more accessible to the city. The rest of the commercial spaces are scattered throughout the city, where GI values are lower than 0.6 and thus not as accessible to the rest of the city (Figure 2).
Firstly, as shown in the Space Syntax result of 1860 Paris (Figure 3), the centrality of the existing north–south axis is reinforced by the addition of a highly integrated road, Blvd. Sébastopol (①, Figure 3), which is inserted between Rue Saint-Denis (②, Figure 3) and Rue Saint Martin-Saint Jacques (③, Figure 3). The accessibility of the core area Les Halles is further enhanced by its transformation into grid-planned market pavilions known as Halles Centrales (④, Figure 3), where every parcel of the market had a GI value from 0.9 to 1.0. Notably, this significant increase in GI also validates that grid planning is indeed the most efficient street network model.
Secondly, the new boulevards are mostly straight and rigid, contributing to the accessibility and centrality of commercial spaces along their routes. In the 1860 result (Figure 3), there were several areas enclosed by the highly integrated boulevards. Blvd. des Capucines-Montmarte-Saint Martin-Temple (⑤, Figure 3), with a total length 8 km, encircles the outer edge of the historical core of Paris, corresponding to the outer edge of the 1st–4th arrondisements and it maintained a GI value of 0.8 throughout its length. Along this ‘ring road’ with high centrality, a series of new commercial spaces were established. On the left bank, an enclosed triangular area is formed, with the boundary roads having a GI value of 0.8 (Figure 3). The triangular area is located in today’s Montparnasse neighborhood. Additionally, Blvd. Saint Germain was constructed, and together with the existing streets Rue de Seine (⑥, Figure 3) and Rue Cuvier (⑦, Figure 3), it formed an enclosed rectangular area along the Seine with highly integrated edges. This area is located in today’s Latin Quarter and Saint-Germain-des-Prés neighborhood. Commercial spaces along the edges of these two enclosures gained high centrality (Figure 3).
Thirdly, there are individual elongated roads with high GI value that extend towards the outer edge of the city, making the commercial spaces that were not originally in central locations more accessible to the city. The segment of Rue Rivoli (⑧, Figure 3), west of Les Halles, stretches for 5.4 km and has a GI value ranging from 0.8 to 1.0. The waterfront route Quay de la Megisserie-Louvre-Tuileries-Conference (⑨, Figure 3) covers a distance of 5.3 km and maintains a GI value of 0.8 to 1.0. Consequently, these boulevards enhance the accessibility of the old commercial spaces, Place Royale, Marché Au Vins, and Marché Saint-Germain (⑩, ⑪, ⑫, Figure 3).
As a result of the expanded network of highly integrated streets in 1860 Paris, most of the marketplaces had high accessibility to the rest of the city, including the existing commercial spaces from the 1690 map and a number of newly built commercial spaces around the new boulevards.
As shown in the Space Syntax result of 2023 Paris (Figure 4), highly integrated streets are concentrated in multiple areas based on the framework of the 1860 results (Figure 3 and Figure 4). Commercial spaces have increased in quantity and are now more dispersed at an urban scale while being more clustered at a local scale. The distribution of commercial spaces is roughly consistent with the concentration of highly integrated streets (Figure 4).
Firstly, the street structure and distribution of commercial spaces in the city core, particularly in the Les Halles area, have changed significantly from the previous results (①, Figure 4). While the previously prominent central north–south axis is still present, commercial spaces now cluster in Les Halles and the central waterfront area. However, the grid structure has been replaced, and the street network has become sparser and lower in GI value.
Secondly, around the outskirts of the historical core, the enclosed region that appeared in 1860 has evolved into an area with a dense road network with high GI values (Figure 3). The area beneath the ‘ring road’ Blvd. des Capucines-Montmarte-Saint Martin- Rue du Temple (②, Figure 4)is now concentrated with both highly integrated streets and a number of large commercial spaces, especially along Blvd Haussmann (③, Figure 4). This vibrant region west of the core of Paris is known as the Saint Georges-Madeleine-Opera neighborhood.
Thirdly, on the left bank, the formerly enclosed triangular area around the Montparnasse neighborhood has now evolved into a center of highly integrated streets and large commercial spaces. Building upon the boulevards constructed in 1860, additional crisscrossing boulevards have been added to the area, including Rue de Rennes (④, Figure 4) and Blvd. Raspail (⑤, Figure 4), which intersects diagonally. Consequently, a number of large commercial spaces are now located at the intersections of highly integrated streets in the Montparnasse region.
In addition to the street clusters, there are also nodal points, which far-reaching roads extend towards the periphery. Pl. de la République, Arc de Triomphe, Gare Montparnasse, and Gare du Nord are some of the nodal points intersecting multiple radiating highly integrated streets (⑥,⑦,⑧,⑨, Figure 4).

3.2. Cluster Analysis

This section involves a cluster analysis of the highly integrated street network from three historical periods based on the output of Space Syntax analysis in Section 3.1. Highly integrated streets are those with Global Integration values from 0.8–1.0 from 1690, 1860, and 2023. The goal is to optimize their clustering and obtain the centroids using statistical methods to identify the street clusters with high economic activity potential.
As depicted in Figure 5b, the graph displays SSE (Sum of Squared Errors) values for cluster numbers ranging from 1 to 10. As the number of clusters increases, the loss function gradually becomes smoother. Based on the Elbow Method, the value of ‘k’ (number of clusters) corresponding to the point where the SSE levels off from the steepest decline is selected. In the case of 1690, when the amount of clusters ‘k’ is set to 3, the loss function stabilizes, and increasing the number of clusters does not lead to significantly more significant changes. Therefore, the highly integrated streets in 1690 can be divided into 3 clusters.
Based on the clustering results, the central cluster ‘b’, which includes Les Halles and the Île de la Cité area, constitutes the absolute core of Paris. Highly integrated streets are not only concentrated in this area but commercial spaces are also exclusively concentrated here. The three clusters are arranged linearly along a well-defined, highly integrated north–south axis. The central cluster is bounded by Rue aux Ours-Michelle comte, which is 1.25 km north of Seine. To the south, the cluster extends to Île de la Cité, while the highly integrated streets on the left bank are classified into the southern cluster.
As shown in Figure 6b, when the amount of clusters ‘k’ is set to 4, further increasing the number of clusters does not significantly affect the loss function, indicating a high level of optimization. Therefore, the highly integrated streets in 1860 are classified into 4 clusters.
Compared with the cluster results in 1690, a new highly integrated street cluster ‘d’ emerges to the west of the three clusters arrayed along the north–south axis ‘a~c’ (Figure 6b). Simultaneously, all four street clusters expand in scope due to the construction of new boulevards reaching out. The configuration of commercial space clusters in 1860 resembles a star shape (Figure 6a), with the center of the ‘star’ located in the Les Halles area, which then extends northwest into Blvd. Haussmann and south into Blvd. St Germain.
Within the north-western cluster ‘d’, numerous commercial spaces are located, and they are all within approximately 1 km of each other, forming the largest interconnected commercial space cluster. This commercial space cluster is situated in today’s Saint Georges-Madeleine-Opera neighborhood.
Additionally, there’s a faint commercial space cluster stretching along the eastern edge of the central street cluster ‘b’, which is detached from the ‘star’ configuration. This commercial space is roughly located in the Quartier du Temple neighborhood, north-east of Paris. Within cluster ‘c’ on the left bank, the southern commercial spaces are spread along the waterfront, encompassing the Latin Quarter and Saint-Germain-des-Prés neighborhood.
As shown in the result, the density of highly integrated streets is still most concentrated at the central cluster ‘b’, consistent with 1690. However, new commercial spaces on the 1860 map accumulated around the core clusters. Additionally, the north-western quarter cluster ‘d’ emerged as the most vibrant and progressive neighborhood. Being a newly established neighborhood, it had a sufficient extent of highly integrated roads to form its own cluster and attract the majority of new commercial spaces in Paris.
As shown in Figure 7c, when the number of clusters is set to 6, the rate of decline becomes stable, indicating a high level of optimization. Therefore, the highly integrated streets in 2023 are classified into 6 clusters.
In the 2023 clustering result, the number of highly integrated street clusters increased from 4 clusters in 1860 to 6 clusters. Interestingly, the linear array of highly integrated clusters along the north–south axis that persisted from 1690 to 1860 is no longer evident in 2023. Instead, cluster ‘b’, located west of the city’s central axis (Figure 7b), became the most prominent street cluster, resembling the profile of cluster ‘d’ in 1860 (Figure 6), which corresponds to the Saint Georges-Madeleine-Opera neighborhood.
Cluster ‘b’ encompassed the largest number of highly integrated roads and hosted the largest cluster of commercial spaces within its scope (Figure 7b). A group of large commercial spaces was located around Blvd. Haussmann, an extension of Blvd Montmartre-Poissonniere from 1860. Another smaller yet robust cluster was situated along Rue Rivoli and Rue Saint-Honoré.
Cluster ‘a’ geographically central in Paris and inheriting much from the old north–south axis, weakened in terms of street centrality (Figure 7b). Its geographical position shifted southward, crossing the Seine River and merging with the Latin Quarter and Saint-Germain-des-Prés neighborhood. Cluster ‘a’ also experienced a decline in commercial activities, with only one cluster located at Les Halles, smaller in scale compared to the commercial clusters in the western cluster ‘b’(Figure 7a).
The southernmost cluster ‘d’ also exhibits strong commercial activities, encompassing most of the Montparnasse neighborhood and part of the Saint-Germain-des-Prés neighborhood (Figure 7a). Large department stores are clustered along Rue de Sèvres-Rue de Babylone and near Gare Montparnasse.
Comparing the commercial space Euclidean distance clustering results from 1860 to 2023, the connections between different clusters have disappeared, and clusters have become more differentiated and segregated from each other. The three most distinct commercial clusters located in zones ‘a’, ‘b’, and ‘d’ are now not directly connected, indicating that these clusters are more than 1 km apart. Since the central cluster in ‘a’ is still located at the old site of Les Halles, the other two clusters are presumed to have sprawled geographically away from the center of Paris. This could also be a result of the reduction in the footprint of commercial space at Les Halles.
Furthermore, as observed from Figure 7a, the clusters of commercial spaces in 2023 are denser and more concentrated compared to the 1860 results. In 1860, the individual threads of Euclidean connections between commercial spaces were still discernible, whereas, in the 2023 result, the Euclidean distances are so closely packed that they appear as hatches of red. In fact, the commercial spaces of 2023 not only increased in number but have also chosen to be located in close proximity to each other, thereby reinforcing the clustering pattern.

4. Discussion

By comparing the results of Space Syntax and Cluster Analysis results from 1690, 1860, and 2023 in Section 3, we can disclose the patterns of the evolution of the location and distribution of commercial spaces. This section highlights two major patterns identified in the quantitative analysis and conducts a multi-disciplinary discussion on how the socioeconomic context of Paris has influenced the process.

4.1. Pattern 1: Full-Scale Optimization of Commercial Space Centrality within the Historical Core of Paris

As background information, the historical core and the new city districts are divided by the city wall of Paris, established in the early 17th century by Louis XIII [57]. This wall was later demolished to make way for the Grand Boulevards commissioned by Louis XIV [33], as depicted on the 1690 map. In 1860, the formerly suburban areas around the historical core were annexed as part of the city of Paris [58] (Figure 8), and Rue de Remparts marked the differentiation between the historical core of Paris, approximately encompassing the 1st–7th district of Paris [59].
When observing the evolution process, a clear trend emerges: a full-scale optimization of commercial space centrality within the historical core of Paris becomes evident (). The number of commercial spaces situated close to high-centrality streets steadily increased over the three historical stages. By 2023, almost all the commercial spaces will be located at highly integrated locations. These results testify principles from both the “Central Place Theory” and “Bid-Rent Theory”, indicating that commercial spaces tend to gravitate toward locations with high centrality and accessibility within urban settings. The full-scale optimization of accessibility and centrality can be interpreted as a consequence of the evolution of both the urban street network and supply chain segmentation.
In 1690 Paris, only 35 out of the 44 identified commercial spaces were located near highly integrated roads (). The central north–south axis of Rue Saint Martin and Rue Saint-Denis had to dominate centrality, and the overall street network consisted of winding medieval streets with low accessibility (Figure 2) [60]. Rue Saint Martin, built by the Romans before the Middle Ages, inherited a military nature characterized by strict straightness [61], contributing to higher GI value. During the pre-industrial era, production was largely domestic, and some of the commercial space locations were constrained either to artisan dwellings or to the transportation and storage of commodities [62]. For example, Place Royale was built along Rue Saint Antoine (GI 0.5), close to the artisan guild of Faubourg Antoine, outside the city gate [33]. Marche au Vins was located at Quai Saint Bernard (GI 0.6) because wines were transported on the Seine by water merchants [63]. Only half of the commercial spaces were fortunate enough to be located around the central axis.
In the mid-19th century, Baron Haussmann implemented a road-building plan known as the grande croisée [64], which substantially improved the accessibility and centrality of commercial space locations and expanded the territory of commercial spaces.
Firstly, the central area of Paris, especially around Les Halles, had already become very crowded as a result of industrialization in the 19th century. To manage the heavy traffic of people and commodities circulating in and out of the core area of Paris, the central North–South thoroughfare of Paris was reinforced with the construction of Blvd. Sébastopol [63]. To accommodate the largely working-class population, Les Halles was transformed into a grid-planned market pavilion known as Halles Centrales [65], with every single parcel having a GI value above 0.9 (Figure 3). This mega-structure with a rigid street network optimized the accessibility of the street blocks in the Les Halles area.
Secondly, in order to promote social mobility among the elites dwelling in different locations of Paris, the grand boulevards opened up the cramped medieval neighborhoods around the urban core and significantly increased the accessibility of existing commercial spaces (Figure 3) [66]. On the left bank, Blvd Saint-Germain (GI 0.9) was constructed to facilitate the social mobility of elites in the Faubourg Saint Germain neighborhood and the Latin Quarter [66,67], which previously had GI values of 0.4–0.5 (Figure 2). As a result, Place Royale, Marché Au Vins, and Marché Saint-Germain, which were previously located amidst inaccessible roads, are now within 300 m of highly integrated roads (Figure 3). Thirdly, in the north-western part of Paris, boulevards were constructed as a result of speculative housing to develop bourgeois neighborhoods, including Saint Georges, Madeleine, Opera, Europe, and others [66]. Private real estate developers collaborated with the government to upgrade the north-western area of Paris by introducing grand tree-lined boulevards, public squares, and elegant apartments to raise property values and sell them to the rising bourgeoisie in Paris.
Furthermore, despite the improvement in the centrality of existing commercial spaces, the new commercial areas exhibited greater flexibility in terms of their locations and were established along boulevards with high GI values. During the ‘proto-industrialization’ period of France in the 18th and 19th centuries, domestic production was replaced by a segmented supply chain. Manufacturing was moved to the suburbs around Paris, and the city area was reserved primarily for trading the products [68]. Therefore, not only did the number of commercial spaces increase in the urban area of Paris, but commercial spaces were also detached from manufacturing, transportation, or storage [69], and they settled near grand boulevards with higher centrality to maximize sales. For example, a group of new commercial spaces, including Marché d’Aguesseau, Opera houses, Théâtre du Gymnase, and Marché du Temple, were established along the ring promenade of Blvd. Des Capucines-Montmarte-Saint Martin, which had a GI value of 0.8–1.0 (Figure 3). Marché des Carmes and Marché à la volaille were established along Blvd. Saint-Germain is on the right bank.
In Paris 2023, virtually all large commercial spaces achieve the highest centrality and accessibility (Figure 4). As the supply chain becomes globalized and production is completely outsourced, the city of Paris becomes an exclusive center for business activities [70,71]. Large retail corporations shape the commercial landscape of the city. Department stores for non-food products like Lafayette Galeries and BHV Marais, managed by the Galeries Lafayette Group, and Le Bon Marché, managed by LVMH, dominate the scene. Additionally, hypermarkets for household products such as Carrefour and Monoprix, as well as electronic retail chain FNAC, have multiple locations in the core of Paris. According to the Bid-rent theory, these large retail companies are able to secure the most central locations in the city at the highest rent [72]. This explains why most of the commercial spaces in the urban core of Paris are situated around streets with the highest GI value (Figure 4).
Last but not least, as shown in Table 2, there’s a significant distinction in accessibility between commercial spaces within and outside the historical core of Paris. Within the historical core of Paris (Figure 8), the accessibility of commercial spaces steadily increases across the historical stages. However, outside the core, commercial spaces are scattered and lack clear connections to the highly integrated streets. Two main contributing factors account for this disparity in and outside the historical core.
First, in 1860, when Baron Haussmann was commissioned to renovate Paris, he invested a tremendous amount of fortune and effort in renovating the historical core of Paris [73]. Therefore, the improvement in the centrality of the street network mostly took place within the historical core. On the other hand, during 1860, even though some of the production had become industrialized, the suburbs were still responsible for agricultural production, a practice known as urban farming [71]. The population residing in the inner suburbs was mostly proletarian [73], in contrast to the bourgeois class within the historical core of Paris. Conversely, in 1860, the commercial spaces would not choose to be located in the suburbs due to a lack of purchasing power and less developed street networks compared to the core area (Figure 3). This disparity began during the mid-19th century and has persisted to the present day.
In conclusion, compared to Akkelies’s study on how ring roads influenced the location pattern of shops [12], this article provides further elaboration on how large-scale urban road renovations have a decisive impact on the centrality and accessibility of commercial centers. Furthermore, this research discovered that supply chain segmentation also contributes to the optimization of the centrality of commercial spaces, as it enables flexible location choices.

4.2. Pattern 2: Fission and Condensation of Commercial Spaces into Multi-centric Clusters and Geographical Dispersal from Central Paris

Comparing the three sets of cluster results in Section 3.2, it’s observed that within the historical core of Paris, the concentric commercial cluster in 1690 (Figure 5a) transformed into a star-shaped cluster in 1860 (Figure 6a), and multiple consolidated and relatively independent commercial clusters in 2023 (Figure 7a). At an urban scale, the commercial space clusters became more dispersed and spread away from the center of Paris. However, at a neighborhood scale, the commercial spaces became more clustered and concentrated. Furthermore, as the urban street network configuration evolved over time, highly integrated streets were classified into an increasing number of clusters (Figure 5b, Figure 6b, and Figure 7b). These results validate the “Principle of Minimum Differentiation”, suggesting that commercial spaces tend to cluster.
Two socioeconomic processes contributed to the fission and condensation of commercial spaces into multi-centric clusters and their geographical dispersal from central Paris. First, the urban core of Paris underwent decentralization and de-industrialization. Second, particular neighborhoods around the core experienced gentrification, leading to an increasingly uneven distribution of wealth in Paris.
According to the analysis results of 1690 (Figure 5), commercial spaces were concentrated along the roads with the highest GI values, Saint-Denis and Rue Saint Martin. They were particularly clustered in the central section, including Les Halles at the intersection with the trading routes Rue Saint Honore and Saint Antoine, as well as marketplaces along the waterfront edges of the River Seine [74]. Les Halles served as a significant commercial center for grain trading, dating back to medieval times and overseen by government officials [75]. Given its role in regulating grain circulation and pricing throughout Paris, Les Halles needed to reach a certain scale to accommodate all grain trading activities [76]. Additionally, during the pre-industrial period, goods were primarily transported by the water merchants traveling on the River Seine [69,71], which led to the concentration of marketplace around the waterfront areas intersecting with the highly integrated Rue Saint Martin and Rue Saint-Denis. Consequently, as shown in Figure 5, the commercial cluster was formed by Les Halles and marketplaces on Île de la Cité.
In the cluster results of 1860, the center of the commercial space configuration remained at Les Halles, but commercial spaces began to sprawl and concentrate in the northwest neighborhood of Saint Georges-Madeleine-Opera. With the industrialization of the city core, the Les Halles region became densely populated with working-class Parisians [77]. To meet the living needs of this large population, Les Halles was expanded, covering an area of approximately 70,000 m2 (Figure 6). However, due to industrialization and increased population density, the living conditions in the Les Halles region deteriorated [65], leading to the gradual loss of its dominance and symbolization of prosperity in the core area [77]. Simultaneously, the Saint-Georges and Madeline neighborhoods in the northwest of the core began to gain prominence due to speculative housing. These areas attracted mostly Bourgeois residents seeking to assert their social status by living in a new fashionable neighborhood [66]. Commercial spaces followed the mobility of the elite class with higher purchasing power, sprawled away from the center of Paris, and moved towards the northwest. Additionally, on the right bank, commercial spaces concentrated in the elite neighborhoods of Saint Germain-Montparnasse and the Latin quarter.
The phenomenon of decentralization of the core and the uneven distribution of purchasing power continued in Paris in 2023. Both of these processes contributed to the consolidation of segregated commercial clusters, shown in Figure 7.
The Central Place Theory indicates that commercial spaces tend to form spatial clusters where the purchasing power of the surrounding population is high, while commercial spaces tend to be more dispersed in areas with lower purchasing power [9]. According to Figure 9, the average household size in the 2nd, 6th, and 9th arrondissements has been consistently lower than 1.80 since 1975, distinguishing them from the surrounding districts [78]. Additionally, in the north-western part and St Germain-Montparnasse area of Paris, median household income is above EUR 43,300 (Figure 10) [79], while in the central part of Paris, household incomes range from EUR 21,600 to EUR 32,500 (Figure 10). Concurrently with the gentrification of the north-western and south-western parts of Paris, the core of Paris experienced a decline in the 1960s. The Les Halles quarter lost 30% of its population from 1968 to 1975 [78]. The housing conditions in the Les Halles area were too old to adequately serve the residents, and 60% of economically active households in Les Halles earned less than the regional average.
As a result, commercial spaces managed by large retail companies concentrated in the northwest of Paris and Saint Germain-Montparnasse to reach their customers. According to the ‘Principle of Minimum Differentiation’ theory, these new commercial clusters entered a virtuous cycle in which the clusters made the location even more attractive, leading to their continued growth [80]. On the other hand, by 1975, the wholesale market had withdrawn from Les Halles, leaving a vacuum at the heart of Paris [81]. Only recently, a redevelopment project for Les Halles was launched and is still under construction to revive the area. Therefore, the commercial spaces are still in the process of growing [82] and appear to be much weaker in comparison to the clusters in the western and southern quarters of Paris (Figure 7).
In conclusion, the cluster analysis results of this study align with findings in a previous study, which testified to the decentralization of commercial spaces from urban centers. However, the Paris study discovered that, although commercial spaces in Paris have undergone a certain degree of decentralization, their expansion still remains within the historical core area. This phenomenon underscores the sustainability of commercial development in the central city area of Paris when compared to other regions.

5. Conclusions

The location theories, including the ‘Central Place Theory’ [9], ‘Bid-rent theory’ [10], and ‘Principle of Minimum Differentiation theory’ [11], laid the groundwork for the significance of locations to commercial activities and indicated basic attributes of commercial space locations. Building on this foundation, research on commercial space locations has primarily focused on an economic perspective, formulating empirical models to evaluate the desirability of commercial spaces. Recent research based on urban planning disciplines, although scientific and visualized, has tended to have a relatively microscopic scope. Therefore, the relationship between commercial space locations and the urban socioeconomic context remains unresolved.
This study investigated the evolution of commercial space locations in 1690, 1860, and Paris in 2023, employing both quantitative analysis and multi-disciplinary discussion. The quantitative analysis of commercial space locations consists of two parts. First, it assesses the accessibility and centrality of commercial space locations from the three historical periods using Space Syntax. Second, it investigates and visualizes the distribution pattern of highly accessible commercial spaces using clustering analysis methods. In the multi-disciplinary discussion, the analysis results from the three historical periods are compared, revealing two observed patterns in the evolution process. One pattern is the full-scale optimization of commercial space centrality within the historical core of Paris, based on the comparison of the Space Syntax results. Combined with the urban historical context of Paris, the first factor that contributed to the accessibility of commercial locations was the implementation of the urban road system, mainly during Haussmann’s administration. Another factor is the change in the industry structure, which made commercial spaces more flexible in choosing locations. Another pattern is the fission and condensation of commercial spaces into multi-centric clusters and geographical dispersal from central Paris. Commercial spaces became more clustered at a neighborhood scale and more dispersed from the center of Paris at an urban scale. This pattern emerged as a result of the ongoing de-industrialization and decentralization of Paris’s historical core area, as well as the shift towards retail activities in commercial spaces.
The historical progression of commercial space locations in Paris yields several universal conclusions that offer guidance for strategic planning of commercial space locations.
Firstly, the preservation and future planning of commercial spaces could be implemented using the framework of city-wide road networks. Our research finding indicates that the transformation of urban road networks enhances centrality and accessibility in Paris’s commercial spaces, highlighting the close relationship between road network configuration and commercial activities. To safeguard or promote commercial activities, it is crucial to start with the road infrastructure. Paris’s ‘Protection du commerce et de l’artisanat’ within the major planning policy document ‘Plan local d’urbanisme’ extends its protection of commercial spaces to the city-scale road network. In contrast, in other cities like Shenzhen, China, commercial space locations appear sporadic, lacking a systematic approach to reservation. This disjointed approach results in fragmentation within the urban layout, impacting accessibility within the city network. Consequently, congestion often surrounds many commercial centers while others face a decline. Moreover, protecting commercial spaces throughout the city-wide road network effectively prevents both decentralization and excessive concentration of businesses. This approach encourages the development of commercial spaces across the city and fosters connections between different commercial districts.
Secondly, detailed building and land use regulations of commercial spaces shall be tailored for different areas within the city. Our research indicates that commercial space distribution tends to be decentralized at the city scale and clustered at the neighborhood scale. This aligns with the theory of the “Principle of minimum differentiation,” where small-scale clustering is challenging to contradict, even though it may lead to some uneven development issues. Therefore, it is essential to develop commercial space regulations tailored to the characteristics of small-scale neighborhoods, such as floor area ratios, building profiles, and the relationship between buildings and streets. By precisely targeting individual areas, policies can encourage commercial space development in areas with limited commercial activity while implementing certain restrictions in saturated areas. This approach promotes a more balanced distribution of commercial spaces throughout the city, enhancing the distinctiveness of each neighborhood.
Last but not least, Paris’s urban planning policy, “Protection du commerce et de l’artisanat” not only preserves the city’s unique character but also sustains the thriving commercial sector for centuries. Moreover, “Protection du commerce et de l’artisanat” is instrumental in facilitating feasible evolution studies. Without the conscious and deliberate protection of the existing and new commercial spaces, the commercial layout in Paris could have undergone abrupt changes rather than the consistent evolution process that allows for pattern analysis.
The study’s limits include limited historical data potentially affecting analysis accuracy. While it acknowledges socioeconomic impacts on commercial space locations, it might not deeply explore their intricate interplay with economic, political, and urban trends. Focusing on specific historical stages may not capture ongoing spatial evolution or consider external factors like tech advancements or the global economy. Future prospects involve broader longitudinal analyses, qualitative data integration, comparing with similar cities, predictive modeling, assessing policy impact, and leveraging advanced geospatial technologies for precision. By addressing these constraints and embracing these prospects, future research can enhance our understanding of commercial space locations for academic and urban planning benefits.

Author Contributions

Conceptualization, J.Z. and J.S.; methodology, J.Z and Z.F.; software, J.Z. and Z.F.; writing—original draft, J.Z. and Z.F.; writing—review and editing, J.Z.; data visualization, J.Z. and Z.F.; supervision, J.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

All the data used are reflected in the article. If you need other relevant data, please contact the author.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

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Figure A1. Johannes de Ram, Lutetiae Parisiorum Universae Gallae Metropolis novissima and accuratissima delineatio, 1690. Source: Gallica Digital Library. Accessed from Public domain, Wikimedia Commons, 2023.
Figure A1. Johannes de Ram, Lutetiae Parisiorum Universae Gallae Metropolis novissima and accuratissima delineatio, 1690. Source: Gallica Digital Library. Accessed from Public domain, Wikimedia Commons, 2023.
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Figure A2. Andriveau-Goujon, Plan géométral de Paris et de ses agrandissments, 1861. Source: David Rumsey Historical Map Collection. Accessed from Public domain, Wikimedia Commons, 2023.
Figure A2. Andriveau-Goujon, Plan géométral de Paris et de ses agrandissments, 1861. Source: David Rumsey Historical Map Collection. Accessed from Public domain, Wikimedia Commons, 2023.
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Figure 1. Research framework by author.
Figure 1. Research framework by author.
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Figure 2. Space Syntax results of 1690 Paris.
Figure 2. Space Syntax results of 1690 Paris.
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Figure 3. Space Syntax results of 1860 Paris.
Figure 3. Space Syntax results of 1860 Paris.
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Figure 4. Space Syntax results of 2023 Paris.
Figure 4. Space Syntax results of 2023 Paris.
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Figure 5. 1690 Cluster Analysis results (a) Superimposed (b) and Euclidean distance clustering of commercial spaces; (b) K- means clustering of highly integrated streets; (c) Elbow Method diagram.
Figure 5. 1690 Cluster Analysis results (a) Superimposed (b) and Euclidean distance clustering of commercial spaces; (b) K- means clustering of highly integrated streets; (c) Elbow Method diagram.
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Figure 6. 1860 Cluster Analysis results (a) Superimposed (b) and Euclidean distance clustering of commercial spaces; (b) K-means clustering of highly integrated streets; (c) Elbow Method diagram.
Figure 6. 1860 Cluster Analysis results (a) Superimposed (b) and Euclidean distance clustering of commercial spaces; (b) K-means clustering of highly integrated streets; (c) Elbow Method diagram.
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Figure 7. 2023 Cluster Analysis results (a) Superimposed (b) and Euclidean distance clustering of commercial spaces; (b) K-means clustering of highly integrated streets; (c) Elbow Method diagram.
Figure 7. 2023 Cluster Analysis results (a) Superimposed (b) and Euclidean distance clustering of commercial spaces; (b) K-means clustering of highly integrated streets; (c) Elbow Method diagram.
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Figure 8. Diagram of the extent of the historical core versus the outer districts of Paris by Author.
Figure 8. Diagram of the extent of the historical core versus the outer districts of Paris by Author.
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Figure 9. Average Parisian Household Size. (a) 1975; (b) 1982. Source: Atelier Parisien d’Urbanisme, data based on [78]. Redrawn by author.
Figure 9. Average Parisian Household Size. (a) 1975; (b) 1982. Source: Atelier Parisien d’Urbanisme, data based on [78]. Redrawn by author.
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Figure 10. Declared household median income in Paris: 2019. Source: Atelier Parisien d’Urbanisme [79].
Figure 10. Declared household median income in Paris: 2019. Source: Atelier Parisien d’Urbanisme [79].
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Table 1. Global Integration Calculation steps in Space Syntax, based on [39].
Table 1. Global Integration Calculation steps in Space Syntax, based on [39].
EquationDescription
M D C = 1 ( k − 1 ) ∑ k d C k
Mean-depth (MD)		k = number of axes in the system,
d = Total depth.
∑ k d C k = Total depth sum from element C to other streets in the network.
R A C = 1 ( M D C − 1 ) ( k − 2 )
Relative Asymmetry (RA)		Normalizes the mean depth measure from zero to one.
R R A C = R A C D k
Real relative asymmetry (RRA)		To eliminate the impact that size can have on the level of relative asymmetry (RA) values within an actual urban street network. Dk is a ‘centrality measure’ that is based on a normalized graph within numerous number of nodes.
Dk = diamond value that balances out the effects that size can have on the relative asymmetry (RA) value.
G I = 1 R R A C
Global Integration (GI)		RRA value has a positive correlation to MD, which means the element is more segregated from a network of streets. Therefore, the GI is calculated to be the reciprocal of the RRA value.
Table 2. Shortest distance between commercial spaces and highly integrated streets.
Table 2. Shortest distance between commercial spaces and highly integrated streets.
169018602023
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N/A 1Sustainability 15 14499 i004Sustainability 15 14499 i005
1 The outer districts were not part of the city of Paris in 1690.
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Zhang, J.; Song, J.; Fan, Z. The Study of Historical Progression in the Distribution of Urban Commercial Space Locations—Example of Paris. Sustainability 2023, 15, 14499. https://doi.org/10.3390/su151914499

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Zhang J, Song J, Fan Z. The Study of Historical Progression in the Distribution of Urban Commercial Space Locations—Example of Paris. Sustainability. 2023; 15(19):14499. https://doi.org/10.3390/su151914499

Chicago/Turabian Style

Zhang, Jingyuan, Jusheng Song, and Zouyang Fan. 2023. "The Study of Historical Progression in the Distribution of Urban Commercial Space Locations—Example of Paris" Sustainability 15, no. 19: 14499. https://doi.org/10.3390/su151914499

APA Style

Zhang, J., Song, J., & Fan, Z. (2023). The Study of Historical Progression in the Distribution of Urban Commercial Space Locations—Example of Paris. Sustainability, 15(19), 14499. https://doi.org/10.3390/su151914499

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