Faster Betweenness Centrality Updates in Evolving Networks

Finding central nodes is a fundamental problem in network analysis. Betweenness centrality is a well-known measure which quantifies the importance of a node based on the fraction of shortest paths going though it. Due to the dynamic nature of many today's networks, algorithms that quickly update centrality scores have become a necessity. For betweenness, several dynamic algorithms have been proposed over the years, targeting different update types (incremental- and decremental-only, fully-dynamic). In this paper we introduce a new dynamic algorithm for updating betweenness centrality after an edge insertion or an edge weight decrease. Our method is a combination of two independent contributions: a faster algorithm for updating pairwise distances as well as number of shortest paths, and a faster algorithm for updating dependencies. Whereas the worst-case running time of our algorithm is the same as recomputation, our techniques considerably reduce the number of operations performed by existing dynamic betweenness algorithms.Comment: Accepted at the 16th International Symposium on Experimental Algorithms (SEA 2017

Scalable Online Betweenness Centrality in Evolving Graphs

Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best known algorithm runs in O(nm) time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper we propose the first truly scalable algorithm for online computation of betweenness centrality of both vertices and edges in an evolving graph where new edges are added and existing edges are removed. Our algorithm is carefully engineered with out-of-core techniques and tailored for modern parallel stream processing engines that run on clusters of shared-nothing commodity hardware. Hence, it is amenable to real-world deployment. We experiment on graphs that are two orders of magnitude larger than previous studies. Our method is able to keep the betweenness centrality measures up to date online, i.e., the time to update the measures is smaller than the inter-arrival time between two consecutive updates.Comment: 15 pages, 9 Figures, accepted for publication in IEEE Transactions on Knowledge and Data Engineerin

Fully-dynamic Approximation of Betweenness Centrality

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 evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in connected graphs after batches of edge insertions. In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of such upper bound. In addition, we extend our former algorithm for semi-dynamic BFS to batches of both edge insertions and deletions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude

Threshold-activated transport stabilizes chaotic populations to steady states

We explore Random Scale-Free networks of populations, modelled by chaotic Ricker maps, connected by transport that is triggered when population density in a patch is in excess of a critical threshold level. Our central result is that threshold-activated dispersal leads to stable fixed populations, for a wide range of threshold levels. Further, suppression of chaos is facilitated when the threshold-activated migration is more rapid than the intrinsic population dynamics of a patch. Additionally, networks with large number of nodes open to the environment, readily yield stable steady states. Lastly we demonstrate that in networks with very few open nodes, the degree and betweeness centrality of the node open to the environment has a pronounced influence on control. All qualitative trends are corroborated by quantitative measures, reflecting the efficiency of control, and the width of the steady state window