Centrality in Modular Networks

Abstract

Identifying influential nodes in a network is a fundamental issue due to its wide applications, such as accelerating information diffusion or halting virus spreading. Many measures based on the network topology have emerged over the years to identify influential nodes such as Betweenness, Closeness, and Eigenvalue centrality. However, although most real-world networks are modular, few measures exploit this property. Recent works have shown that it has a significant effect on the dynamics on networks. In a modular network, a node has two types of influence: a local influence (on the nodes of its community) through its intra-community links and a global influence (on the nodes in other communities) through its inter-community links. Depending of the strength of the community structure, these two components are more or less influential. Based on this idea, we propose to extend all the standard centrality measures defined for networks with no community structure to modular networks. The so-called "Modular centrality" is a two dimensional vector. Its first component quantifies the local influence of a node in its community while the second component quantifies its global influence on the other communities of the network. In order to illustrate the effectiveness of the Modular centrality extensions, comparison with their scalar counterpart are performed in an epidemic process setting. Simulation results using the Susceptible-Infected-Recovered (SIR) model on synthetic networks with controlled community structure allows getting a clear idea about the relation between the strength of the community structure and the major type of influence (global/local). Furthermore, experiments on real-world networks demonstrate the merit of this approach.

References in corpus (9)

• Uncovering the overlapping community structure of complex networks in nature and society
• Finding community structure in networks using the eigenvectors of matrices
• Maps of random walks on complex networks reveal community structure
• Benchmark graphs for testing community detection algorithms
• Community detection in networks: A user guide
• Vital nodes identification in complex networks
• A Classification for Community Discovery Methods in Complex Networks
• Adaptive model for recommendation of news
• Immunization Strategies Based on the Overlapping Nodes in Networks with Community Structure

Cited by in corpus (9)

• On community structure in complex networks: challenges and opportunities
• Measuring Node Contribution to Community Structure with Modularity Vitality
• Characterizing the Interactions Between Classical and Community-aware Centrality Measures in Complex Networks
• Interplay Between Hierarchy and Centrality in Complex Networks
• Map Equation Centrality: Community-aware Centrality based on the Map Equation
• Lexical Sorting Centrality to Distinguish Spreading Abilities of Nodes in Complex Networks under the Susceptible-Infectious-Recovered (SIR) Model
• Identifying Influential Nodes Using Overlapping Modularity Vitality
• Estimating the Expected Influence Capacities of Nodes in Complex Networks under the Susceptible-Infectious-Recovered (SIR) Model
• Binomial Tails for Community Analysis