[Paper Review] Network centrality: an introduction

Francisco A. Rodrigues|arXiv (Cornell University)|Jan 22, 2019

Complex Network Analysis Techniques4 citations

TL;DR

This paper provides a comprehensive review of network centrality measures in complex networks, explaining their theoretical foundations, applications in dynamical processes like epidemic spreading and synchronization, and their use in neuroscience and systems biology. It highlights that degree, betweenness, eigenvector, and closeness centrality capture distinct structural roles, with central nodes significantly influencing system dynamics and disease propagation.

ABSTRACT

Centrality is a key property of complex networks that influences the behavior of dynamical processes, like synchronization and epidemic spreading, and can bring important information about the organization of complex systems, like our brain and society. There are many metrics to quantify the node centrality in networks. Here, we review the main centrality measures and discuss their main features and limitations. The influence of network centrality on epidemic spreading and synchronization is also pointed out in this chapter. Moreover, we present the application of centrality measures to understand the function of complex systems, including biological and cortical networks. Finally, we discuss some perspectives and challenges to generalize centrality measures for multilayer and temporal networks.

Motivation & Objective

• To review and compare the most widely used network centrality measures and their theoretical foundations.
• To examine how centrality influences dynamical processes such as epidemic spreading and synchronization in complex networks.
• To demonstrate the utility of centrality measures in understanding brain function and diagnosing neurological disorders like schizophrenia.
• To identify open challenges in extending centrality measures to multilayer and temporal networks.
• To guide researchers in selecting appropriate centrality metrics based on application-specific network dynamics.

Proposed method

• Systematic review of 10+ centrality measures, including degree, betweenness, eigenvector, and closeness centrality, with mathematical definitions using adjacency matrices.
• Application of centrality metrics to real-world networks: brain networks (fMRI data), climate systems (ocean currents), world trade, and air transportation networks.
• Use of network-theoretic models to simulate epidemic spreading and Kuramoto synchronization, linking node centrality to critical thresholds.
• Analysis of neuroimaging data from 1003 subjects to correlate age-related changes in centrality with cognitive decline.
• Evaluation of centrality-based diagnostics in schizophrenia using k-core, closeness, and accessibility measures.
• Discussion of emerging network types—multilayer and temporal networks—and adaptation of centrality measures to these structures.

Experimental results

Research questions

• RQ1 Which centrality measures best predict the spread of epidemics in complex networks?
• RQ2 How does network centrality influence the onset of synchronization in coupled oscillator systems?
• RQ3 To what extent can centrality metrics serve as biomarkers for neurological disorders like schizophrenia?
• RQ4 How do centrality measures differ in their sensitivity to age-related changes in brain networks?
• RQ5 What are the key challenges in generalizing centrality measures to multilayer and time-varying (temporal) networks?

Key findings

• Degree centrality is a local measure and may misidentify central nodes in networks with peripheral hubs, as seen in Figure 2(a).
• In brain networks, regional hubs in the precuneus and posterior cingulate cortex are highly central, and their degree centrality decreases with age, while eigenvector centrality remains stable.
• Schizophrenic patients exhibit significantly higher variance in closeness centrality and accessibility, but lower average k-core values, enabling 90% sensitivity and 74% specificity in automated diagnosis.
• Betweenness centrality identifies the backbone of global ocean surface circulation, with high-betweenness nodes forming the primary pathways for heat and nutrient transport.
• In air transportation networks, the most connected cities are not always the most central due to the network's multi-community structure.
• Centrality measures such as eigenvector and closeness centrality are more informative than degree centrality in detecting subtle network-level changes in neurological conditions.