Centrality in social networks conceptual clarification

TL;DR: A randomized approximation algorithm for centrality in weighted graphs is described that estimates the centrality of all vertices with high probability within a (1 + ∈) factor in near-linear time for graphs exhibiting the small world phenomenon.

TL;DR: A novel paradigm was developed to study the behavior of groups of networked people searching a problem space and it was demonstrated that the optimal network structure depends on the problem space being explored, with networks that incorporate spatially based cliques having an advantage for problems that benefit from broad exploration.

TL;DR: A new measure is proposed that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states, that can be extended to include random walk based definitions and its computational complexity is shown to be of the same order as that of betweenness centrality.

TL;DR: It is found that centrality measures are generally positively correlated to each other, the strength of these correlations varies across networks, and network modularity plays a key role in driving these cross-network variations.

TL;DR: It is shown that the optimum location of a switching center is always at a vertex of the communication network while the best location for the police station is not necessarily at an intersection.