Alexander G. Nikolaev

Efficient algorithms for incremental all pairs shortest paths, closeness and betweenness in social network analysis

One of the biggest challenges in today’s social network analysis (SNA) is handling dynamic data. Real-world social networks evolve with time, forcing their corresponding graph representations to dynamically update by addition or deletion of edges/nodes. Consequently, a researcher is often interested in fast recomputation of important SNA metrics pertaining to a network. Recomputations of SNA metrics are expensive. Use of dynamic algorithms has been found as a solution to this problem. For calculating closeness and betweenness centrality metrics, computations of all pairs shortest paths (APSP) are needed. Thus, to compute these SNA metrics dynamically, APSP are needed to be computed dynamically. This paper presents fast incremental updating algorithms along with the time complexity results for APSP, closeness centrality and betweenness centrality, considering two distinct cases: edge addition and node addition. The following time complexity results are presented: (1) The incremental APSP algorithm runs in

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O(n^2)

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O(n2) time (

Probabilistic graphical models in modern social network analysis

\Omega (n^2)

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Ω(n2) is the theoretical lower bound of the APSP problem), (2) The incremental closeness algorithm that runs in