Abstract
Understanding the importance of links in transmitting information in a network can provide ways to hinder or postpone ongoing dynamical phenomena like the spreading of epidemic or the diffusion of information. In this work, we propose a new measure based on stochastic diffusion processes, the transmission centrality, that captures the importance of links by estimating the average number of nodes to whom they transfer information during a global spreading diffusion process. We propose a simple algorithmic solution to compute transmission centrality and to approximate it in very large networks at low computational cost. Finally we apply transmission centrality in the identification of weak ties in three large empirical social networks, showing that this metric outperforms other centrality measures in identifying links that drive spreading processes in a social network.
Highlights
The importance of nodes and links in networks is commonly measured through centrality measures
Centrality measures based on global information about the network structure, like betweenness and closeness centrality [1, 2], Katz centrality [3], k-shell index [4, 5], subgraph centrality [6] and induced centrality measures [7] may better characterize the overall importance of a node or link
5 Discussion In this study we introduced a new link centrality measure, called transmission centrality, which sensitively quantifies the importance of links in global diffusion processes
Summary
The importance of nodes and links in networks is commonly measured through centrality measures. Their definitions generally rely on local and/or global structural information. These measures cannot provide information on which nodes or links play global roles in the network structure. Centrality measures based on global information about the network structure, like betweenness and closeness centrality [1, 2], Katz centrality [3], k-shell index [4, 5], subgraph centrality [6] and induced centrality measures [7] may better characterize the overall importance of a node or link. Effective algorithms for approximating these quantities have recently been proposed [8, 9], estimating these measures in large scale networks is still computationally challenging
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