Application of Graph Theory for Identifying Connectivity Patterns in Human Brain Networks: A Systematic Review

Abstract

Background: Analysis of the human connectome using functional magnetic resonance imaging (fMRI) started in the mid-1990s and attracted increasing attention in attempts to discover the neural underpinnings of human cognition and neurological disorders. In general, brain connectivity patterns from fMRI data are classified as statistical dependencies (functional connectivity) or causal interactions (effective connectivity) among various neural units. Computational methods, especially graph theory-based methods, have recently played a significant role in understanding brain connectivity architecture. Objectives: Thanks to the emergence of graph theoretical analysis, the main purpose of the current paper is to systematically review how brain properties can emerge through the interactions of distinct neuronal units in various cognitive and neurological applications using fMRI. Moreover, this article provides an overview of the existing functional and effective connectivity methods used to construct the brain network, along with their advantages and pitfalls. Methods: In this systematic review, the databases Science Direct, Scopus, arXiv, Google Scholar, IEEE Xplore, PsycINFO, PubMed, and SpringerLink are employed for exploring the evolution of computational methods in human brain connectivity from 1990 to the present, focusing on graph theory. The Cochrane Collaboration's tool was used to assess the risk of bias in individual studies. Results: Our results show that graph theory and its implications in cognitive neuroscience have attracted the attention of researchers since 2009 (as the Human Connectome Project launched), because of their prominent capability in characterizing the behavior of complex brain systems. Although graph theoretical approach can be generally applied to either functional or effective connectivity patterns during rest or task performance, to date, most articles have focused on the resting-state functional connectivity. Conclusions: This review provides an insight into how to utilize graph theoretical measures to make neurobiological inferences regarding the mechanisms underlying human cognition and behavior as well as different brain disorders.

Keywords: brain connectivity; brain networks; connectome; effective connectivity; fMRI; functional connectivity; graph theory; small-world.

Figure 1

Taxonomy of existing methods for modeling functional and effective connectivity patterns using fMRI. Each of the identified methods can be represented in terms of a graph, where the nodes correspond to cortical or subcortical regions and the edges represent (directed or undirected) connections (Bullmore and Sporns, 2012); thereby all of them can be further examined with graph-theoretic measures.

Figure 2

A network can be designed as binary (A) or weighted (B) graphs, and can represent the direction of causal effects (C,D) among different regions.

Figure 3

Schematic representation of brain network construction and graph theoretical analysis using fMRI data. After processing (B) the raw fMRI data (A) and division of the brain into different parcels (C), several time courses are extracted from each region (D) so that they can create the correlation matrix (E). To reduce the complexity and enhance the visual understanding, the binary correlation matrix (F), and the corresponding functional brain network (G) are constructed, respectively. Eventually, by quantifying a set of topological measures, graph analysis is performed on the brain's connectivity network (H).

Figure 4

Summary of global graph measures. (A) Segregation measures include clustering coefficient, which quantify how much neighbors of a given node are interconnected and measures the local cliquishness (i.e., the extent to which the neighbors of a node can build a complete graph); modularity, which is related to clusters of nodes, called modules, that have dense interconnectivity within clusters but sparse connections between nodes in different clusters. On the one hand, dense communications within a certain module increase the local clustering and, consequently, enhance the efficiency of information transmission in the given module. On the other hand, a few connections between different modules integrate the global information flow, which is associated with a reduction in the average path length in the graph (B) Integration measure include characteristic path length, which measures the potential for information transmission, determined as the average shortest path length across all pairs of nodes. (C) A regular network (left) displays a high clustering coefficient and a long average path length, while a random network (right) displays a low clustering coefficient and a short average path length. A small-world network (middle) illustrates an intermediate balance between regular and random networks (i.e., they consist of many short-range links alongside a few long-range links), reflecting a high clustering coefficient and a short path length. (D) The assortativity index measures the extent to which a network can resist failures in its main components (i.e., its vertices and edges). Notably, communication between hubs in assortative networks leads to covering each other's activities when a particular hub crashes, but the performance in disassortative networks will drop sharply due to the presence of vulnerable hubs.

Figure 5

Basic concept of network centralities. (A) Hubs (connector or provincial) refer to nodes with a high nodal centrality, which can be identified using different measures. (B) The degree centrality is defined as the number of node's neighbors. The betweenness centrality measures the node's role in acting as a bridge between separate clusters by computing the ratio of all shortest paths in the network that contain a given node. The closeness centrality quantifies how fast a given node in a connected graph can access all other nodes, hence the more central a node is, the closer it is to all other nodes. The eigenvector centrality is a self-referential measure of centrality that considers the quality of a link, so that being connected to a central node increases one's centrality in turn; the red colored node is more central than the gray colored node, although their degrees are equal. The participation coefficient of a node represents the distribution of its connections among separate modules. PageRank is a variant of eigenvector centrality, used by Google Search to determine a page's importance; the PageRank of an undirected graph is statistically similar to the degree centrality, but they are generally distinct. Note that the size of the nodes in all cases is proportional to the node degree, and the red nodes (except in the eigenvalue centrality) are the most central with respect to the corresponding definition of centrality, even though their degree are low.

Figure 6

Flow diagram of the methodology and selection processes used in this review. It follows the guidelines of PRISMA (Moher et al., 2010).

Figure 7

Categorization of included studies.

Figure 8

Assessing the risk of bias using the Cochrane collaboration's tool.

Figure 9

Selected papers per year (publishing trend).

Figure 10

Pareto analysis of top keywords. fMRI, Functional magnetic resonance imaging; DMN, default mode network; ADHD, Attention-deficit/hyperactivity disorder; MCI, Mild cognitive impairment; SVM, Support vector machine; ICA independent component analysis.

Figure 11

Frequency of the authors in the references.