Betweenness centrality in large complex networks

By Marc Barthelemy. 2003

773 citations recorded by the source corpus.

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 $\delta\geq (\gamma + 1)/2$. If the scale free network is a tree, then we have the equality $\delta = (\gamma + 1)/2$.

Subfields: Condensed Matter Physics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7f0b43701dd32bbf821ef0cd9663f8fc841abe35

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In Condensed Matter Physics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Network topology reveals high connectance levels and few key microbial genera within soils (2014, background): “A number of studies have been performed using the degree centrality to identify hubs in networks but we decided to use BC and CC because the degree is a local quantity which does not inform about the importance of a node in the network (Barthélemy, 2004).”
What makes a species central in a cleaning mutualism network (2010, background): “The ‘betweenness centrality’ (BC) measures the extent to which a species lies on the shortest paths among other pairs of species (Newman 2003, Barthélemy 2004, Jordán et al. 2006).”
Synchronization in complex networks (2008, background): “However, the load of a node in SF networks is closely related to the degree (Barthélemy, 2004; Goh et al., 2001), i.e., nodes with large degrees or links connecting nodes with large degrees have, on average, a large load.”
Customer churn prediction in telecom using machine learning in big data platform (2019, background): “For example, Barthelemy [10] proposed a new algorithm to reduce the complexity of calculating the Betweenness centrality from O(n3) to O(n2).”
Water for food: The global virtual water trade network (2011, background): “[31] While node degree is the simplest proxy for centrality, it is a local measure that does not provide any information about the importance of the node within the global structure [Barthelemy, 2004].”
OSMnx: New methods for acquiring, constructing, analyzing, and visualizing complex street networks (2016, background): “Betweenness centrality evaluates the number of shortest paths that pass through each node or edge (Barthélemy, 2004).”