On Local and Global Centrality in Large Scale Networks
  Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes in a network, a classical metric is centrality within which there are multiple specific instances including degree centrality, closeness centrality, betweenness centrality and more. As of today, existing algorithms to identify nodes with high centrality measures operate upon the entire (or rather global) network, resulting in high computational complexity. In this paper, we design efficient algorithms for determining the betweenness centrality in large scale networks by taking advantage of the modular topology exhibited by most of these large scale networks. Very briefly, modular topologies are those wherein the entire network appears partitioned into distinct modules (or clusters or communities), wherein nodes within the module (that likely share highly similar profiles) have dense connections between them, while connections across modules are relatively sparse. Using a novel adaptation of Dijkstra's shortest path algorithm, and executing it over local modules and over sparse edges between modules, we design algorithms that can correctly compute the betweenness centrality much faster than existing algorithms. To the best of our knowledge, ours is the first work that leverage modular topologies of large scale networks to address the centrality problem, though here we mostly limit our discussions to social networks. We also provide more insights on centrality in general, and also how our algorithms can be used to determine other centrality measures. 
Sima Das
cs.SI physics.soc-ph