Approximating Betweenness Centrality in Fully Dynamic Networks

Abstract

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in networks that change over time.In this paper we propose the first betweenness centrality approximation algorithms with a provable guarantee on the maximum approximation error for dynamic networks. Several new intermediate algorithmic results contribute to the respective approximation algorithms: (i) new upper bounds on the vertex diameter, (ii) the first fully-dynamic algorithm for updating an approximation of the vertex diameter in undirected graphs, and (iii) an algorithm with lower time complexity for updating single-source shortest paths in unweighted graphs after a batch of edge actions.Using approximation, our algorithms are the first to make in-memory computation of betweenness in dynamic networks with millions of edges feasible. Our experiments show that our algorithms can achieve substantial speedups compared to recomputation, up to several orders of magnitude. Moreover, the approximation accuracy is usually significantly better than the theoretical guarantee in terms of absolute error. More importantly, for reasonably small approximation error thresholds, the rank of nodes is well preserved, in particular for nodes with high betweenness.

Dynamical algorithms for data mining and machine learning over dynamic graphs

“…Bergamini and Meyerhenke (2016) proposed one of the first dynamical approximate algorithms for estimating betweenness centrality. Their algorithm updates the scores after one or a batch of edge update operations (i.e., edge addition, edge deletion, edge weight change).…”

“…Since exact computation of VD is computationally heavy, RK uses upper bounds that can be computed in O ( n + m ) time. After one or a batch of graph update operations, the algorithm of Bergamini and Meyerhenke (2016) updates the used upper bound for VD and the set S of sampled shortest paths stored to estimate betweenness scores. Let be the set of all shortest paths from s to t in the updated graph.…”

Enabling massive deep neural networks with the GraphBLAS

“…Graphs are among the most important abstract data structures in computer science, and the algorithms that operate on them are critical to applications in bioinformatics, computer networks, and social media [32]- [36]. Graphs have been shown to be powerful tools for modeling complex problems because of their simplicity and generality [37], [38]. For this reason, the field of graph algorithms has become one of the pillars of theoretical computer science, performing research in such diverse areas as combinatorial optimization, complexity theory, and topology.…”

Comparing the speed and accuracy of approaches to betweenness centrality approximation

“…Like Yoshida's method, the HEDGE algorithm introduced in [47] works with evolving networks and has provable bounds on the accuracy of the approximation. An additional algorithm with applicability to dynamic networks is described in [48].…”