Betweenness Centrality in Large Complex Networks

Abstract

We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\eta$. We find that for trees or networks with a small loop density $\eta =2$ while a larger density of loops leads to $\eta <2$. For scale-free networks characterized by an exponent $\gamma$ which describes the connectivity distribution decay, the BC is also distributed according to a power law with a non universal exponent $\delta$. We show that this exponent $\delta$ must satisfy the exact bound $\delta \ge (\gamma +1)/2$. If the scale free network is a tree, then we have the equality $\delta =(\gamma +1)/2$.

6 pages, 5 figures, revised version

References in corpus (12)

• Emergence of scaling in random networks
• Epidemic spreading in scale-free networks
• The diameter of the world wide web
• Evolution of networks
• Classes of behavior of small-world networks
• Attack vulnerability of complex networks
• Breakdown of the Internet under intentional attack
• Universal Behavior of Load Distribution in Scale-free Networks
• Large-scale topological and dynamical properties of Internet
• Classification of scale-free networks
• Comment on: 'Universal Behavior of Load Distribution in Scale-free Networks'
• Reply to "Comment on 'Universal Behavior of Load Distribution in Scale-Free Networks'"

Cited by in corpus (50)

• Synchronization in complex networks
• OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks
• Statistical physics of vaccination
• Robustness and resilience of complex networks
• Efficient routing on complex networks
• Statistical properties of sampled networks
• Statistical analysis of 22 public transport networks in Poland
• Customer churn prediction in telecom using machine learning and social network analysis in big data platform
• From the betweenness centrality in street networks to structural invariants in random planar graphs
• A Multi-Scale Analysis of 27,000 Urban Street Networks: Every US City, Town, Urbanized Area, and Zillow Neighborhood
• Measuring the Complexity of Urban Form and Design
• The effects of spatial constraints on the evolution of weighted complex networks
• Exploring networks with traceroute-like probes: theory and simulations
• Measuring urban road network resilience to extreme events: an application for urban floods
• Efficiency of attack strategies on complex model and real-world networks
• Random walk centrality in interconnected multilayer networks
• Global efficiency of local immunization on complex networks
• Enhance synchronizability by structural perturbations
• Extreme events on complex networks
• Relations between Average Distance, Heterogeneity and Network Synchronizability
• Co-evolution of density and topology in a simple model of city formation
• Two betweenness centrality measures based on Randomized Shortest Paths
• K-Core based Temporal Graph Convolutional Network for Dynamic Graphs
• Universal scaling of distances in complex networks
• Efficient routing strategies in scale-free networks with limited bandwidth
• Analytic solution of a static scale-free network model
• Traffic dynamics in scale-free networks with limited packet-delivering capacity
• Resilient by Design: Simulating Street Network Disruptions across Every Urban Area in the World
• Forecasting failure locations in two-dimensional disordered lattices
• Network Inference from TraceRoute Measurements: Internet Topology `Species'
• Effect of edge removal on topological and functional robustness of complex networks
• Superspreading k-cores at the center of COVID-19 pandemic persistence
• Topologies and Laplacian spectra of a deterministic uniform recursive tree
• Socioeconomic Networks with Long-Range Interactions
• Abrupt transition due to non-local cascade propagation in multiplex systems
• Multiple abrupt phase transitions in urban transport congestion
• Central loops in random planar graphs
• Betweenness centrality in dense spatial networks
• Networking genetic regulation and neural computation: Directed network topology and its effect on the dynamics
• Optimal transport on supply-demand networks
• Transmission of packets on a hierarchical network: Statistics and explosive percolation
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Transitions in spatial networks
• Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks
• Morphological organization of point-to-point transport in complex networks
• Mining Influential Spreaders in Complex Networks by an Effective Combination of the Degree and K-Shell
• The behavior of rich-club coefficient in scale-free networks
• A statistical mechanics investigation of Unfolded Protein Response across organisms
• Shortest-path percolation on scale-free networks
• About the Influence of Workflow Topology on Task Intensity Prediction through Graph Learning