Graph Theory Measures and Their Application to Neurosurgical Eloquence
Abstract
:Simple Summary
Abstract
1. Introduction
2. Connectomics of the Brain
2.1. Graphing Structural Connectivity
2.2. Graphing Functional Connectivity
3. Parcellating the Brain
4. Hubness and Centrality
4.1. Types of Centrality
4.2. Centrality as a Measure of Hubness
5. Eloquence in Neurosurgery
5.1. Individual Variability
5.2. Hubness as a Measure of Eloquence
6. Emerging Difficulties and New Prospects Moving Forward
6.1. Difficulties of Analysis and Interpretation for Patients
6.2. Clinical Graph Theory on the Horizon
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Term | Definition | Examples of Methods Used for Its Acquisition |
---|---|---|
Adjacency matrix | A summary of all connections between each pair of nodes. | -- |
Centrality | Measure of the importance of a node within the network. | Degree, betweenness, closeness, and PageRank |
Connection | A relation or interaction between two nodes in the network. Connections may be binary or weighted and can be directed or undirected. They are referred to as edges in graphs. | Diffusion MRI (structural connectivity), functional MRI (functional connectivity) |
Connectome | A map of all of the anatomical connections of the brain. | |
Degree | The number of edges attached to a node. | Degree centrality |
Edge | A term in graph theory to refer to a connection between two nodes. | Diffusion MRI (structural connectivity), functional MRI (functional connectivity) |
Functional connectivity | The statistical correlation of co-activation of two nodes in the network. | fMRI, MEG, EEG |
Graph | A mathematical representation of a network, comprising of nodes and edges. | -- |
Hub | A node with a central role in the network determined by its possession of links that greatly exceed the average, often defined through centrality. | Centrality |
Module | A group of nodes within a graph which have many mutual connections, and few connections to nodes outside their module. | Number of links in the network; number of links between nodes in a specific module, summation of the degrees of the node within the module |
Parcellation | An anatomical or functional division of the brain, which can be used as a node in graph theory. | Atlas-based schemes (Glasser, AAL, Gordon), |
Participation coefficient | A measure of the distribution of a node’s edges across the modules within the graph. | Number of links to other nodes in a module; degree of the node |
Path length | The number of edges which must be traversed to travel from one node to another node in the network. While this term technically refers to pathways in which the edges and nodes are traversed only once, it is commonly used in the literature to define any successive edges from one node to another. If there are multiple paths between two nodes, the path length may refer to the average length of all these paths. | The inverse of the average path length within the network, or the average distance between each pair of nodes, reflects the efficiency of information transferring in the entire network |
Percolation | The method of deleting nodes within a network to model the effects of lesions on network topology. | Performed on an existing connectome to virtually emulate a lesion |
Structural connectivity | The anatomical connections between the nodes of the network. | Diffusion MRI |
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Tanglay, O.; Dadario, N.B.; Chong, E.H.N.; Tang, S.J.; Young, I.M.; Sughrue, M.E. Graph Theory Measures and Their Application to Neurosurgical Eloquence. Cancers 2023, 15, 556. https://doi.org/10.3390/cancers15020556
Tanglay O, Dadario NB, Chong EHN, Tang SJ, Young IM, Sughrue ME. Graph Theory Measures and Their Application to Neurosurgical Eloquence. Cancers. 2023; 15(2):556. https://doi.org/10.3390/cancers15020556
Chicago/Turabian StyleTanglay, Onur, Nicholas B. Dadario, Elizabeth H. N. Chong, Si Jie Tang, Isabella M. Young, and Michael E. Sughrue. 2023. "Graph Theory Measures and Their Application to Neurosurgical Eloquence" Cancers 15, no. 2: 556. https://doi.org/10.3390/cancers15020556
APA StyleTanglay, O., Dadario, N. B., Chong, E. H. N., Tang, S. J., Young, I. M., & Sughrue, M. E. (2023). Graph Theory Measures and Their Application to Neurosurgical Eloquence. Cancers, 15(2), 556. https://doi.org/10.3390/cancers15020556