Computing Top-k Closeness Centrality in Fully-dynamic Graphs

Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k most central nodes and not all closeness values. Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks. However, for networks that evolve over time, no dynamic top-k closeness algorithm exists that improves on static recomputation. In this paper, we present several techniques that allow us to efficiently compute the k nodes with highest (harmonic) closeness after an edge insertion or an edge deletion. Our algorithms use information obtained during earlier computations to omit unnecessary work. However, they do not require asymptotically more memory than the static algorithms (i. e., linear in the number of nodes). We propose separate algorithms for complex networks (which exhibit the small-world property) and networks with large diameter such as street networks, and we compare them against static recomputation on a variety of real-world networks. On many instances, our dynamic algorithms are two orders of magnitude faster than recomputation; on some large graphs, we even reach average speedups between 10 and 10. ∗This work is partially supported by German Research Foundation (DFG) grant ME 3619/3-1 within the Priority Programme 1736 Algorithms for Big Data. 1 ar X iv :1 71 0. 01 14 3v 1 [ cs .D S] 3 O ct 2 01 7 October 4, 2017, 0:52