Fully-Dynamic Approximation of Betweenness Centrality

Computational Social Networks

BC(v) = s� =v� =t σ st (v) σ st ,

2012 International Conference on Privacy, Security, Risk and Trust and 2012 International Confernece on Social Computing, 2012

We propose and evaluate two complementary heuristics to speed up exact computation of the shortest-path betweenness centrality. Both heuristics are relatively simple adaptations of the standard algorithm for betweenness centrality. Consequently, they generalize the computation of edge betweenness and most other variants, and can be used to further speed up betweenness estimation algorithms, as well. In the first heuristic, structurally equivalent vertices are contracted based on the observation that they have the same centrality and also contribute equally to the centrality of others. In the second heuristic, we first apply a linear-time betweenness algorithm on the block-cutpoint tree and then compute the remaining contributions separately in each biconnected component. Experiments on a variety of large graphs illustrate the efficiency and complementarity of our heuristics.

Algorithms and models for the web-graph, 2007

Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O (nm) time for unweighted graphs and O (nm+ n 2 logn) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are also the worst-case time bounds for computing the betweenness score of a single vertex. In this paper, we present a novel ...

2016

The neighborhood function measures node centrality in graphs by measuring how many nodes a given node can reach in a certain number of steps. The neighborhood function can for example be used to find central nodes or the degree of separation. The state-of-the-art algorithm, called HyperANF (Hyper Approximate Neighborhood Function), can calculate an approximate neighborhood function for graphs with billions of nodes within hours using a standard workstation [P. Boldi, M. Rosa, and S. Vigna, “Hyperanf: Approximating the neighbourhood function of very large graphs on a budget,” CoRR, vol. abs/1011.5599, 2010]. However, it only supports static graphs. If the neighborhood function should be calculated on a dynamic graph, the algorithm has to be re-run at any change in the graph. We develop a novel algorithm called Dynamic Approximate Neighborhood Function (DANF) which extends HyperANF to support dynamic graphs. In our algorithm, all relevant nodes are updated when new edges are added to ...

IEEE Transactions on Big Data, 2018

This paper presents a network-based template for analyzing largescale dynamic data. Specifically, we propose a novel shared-memory parallel algorithm for updating tree-based structures or properties, such as connected components (CC) and minimum spanning trees (MST), on dynamic networks. The underlying idea is to update the information in a rooted tree data structure that stores the edges of the network that are most relevant to the analysis. Extensive experiments on real-world and synthetic networks demonstrate that, with the exception of the inherently sequential component for creating the rooted tree, our proposed updatiing algorithm is scalable and, in most cases, also requires significantly less memory, energy, and time than recomputing-from-scratch algorithm. To the best of our knowledge, this is the first parallel algorithm for updating MST on weighted dynamic networks. The rooted-tree based framework that we propose in this paper can be extended for updating other weighted and unweighted tree-based properties such as single source shortest path and betweenness and closeness centrality.

Analysis of social networks is challenging due to the rapid changes of its members and their relationships. For many cases it impractical to recompute the metric of interest, therefore, streaming algorithms are used to reduce the total runtime following modifications to the graph. Centrality is often used for determining the relative importance of a vertex or edge in a graph. The vertex Betweenness Centrality is the fraction of shortest paths going through a vertex among all shortest paths in the graph. Vertices with a high betweenness centrality are usually key players in a social network or a bottleneck in a communication network. Evaluating the betweenness centrality for a graph G = (V, E) is computationally demanding and the best known algorithm for unweighted graphs has an upper bound time complexity of O(V 2 + V E). Consequently, it is desirable to find a way to avoid a full re-computation of betweenness centrality when a new edge is inserted into the graph. In this work, we give a novel algorithm that reduces computation for the insertion of an edge into the graph. This is the first algorithm for the computation of betweenness centrality in a streaming graph. While the upper bound time complexity of the new algorithm is the same as the upper bound for the static graph algorithm, we show significant speedups for both synthetic and real graphs. For synthetic graphs the speedup varies depending on the type of graph and the graph size. For synthetic graphs with 16384 vertices the average speedup is between 100X − 400X. For five different real world collaboration networks the average speedup per graph is in range of 36X − 148X.

Parallel Processing and Applied Mathematics

Dynamic graphs can capture changing relationships in many real datasets that evolve over time. One of the most basic questions about networks is the identification of the "most important" vertices in a network. Measures of vertex importance called centrality measures are used to rank vertices in a graph. In this work, we focus on Katz Centrality. Typically, scores are calculated through linear algebra but in this paper we present an new alternative, agglomerative method of calculating Katz scores and extend it for dynamic graphs. We show that our static algorithm is several orders of magnitude faster than the typical linear algebra approach while maintaining good quality of the scores. Furthermore, our dynamic graph algorithm is faster than pure static recomputation every time the graph changes and maintains high recall of the highly ranked vertices on both synthetic and real graphs.

Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining - ASONAM '13, 2013

Automation of data collection using online resources has led to significant changes in traditional practices of social network analysis. Social network analysis has been an active research field for many decades; however, most of the early work employed very small datasets. In this paper, a number of issues with traditional practices of social network analysis in the context of dynamic, large-scale social networks are pointed out. Given the continuously evolving nature of modern online social networking, we postulate that social network analysis solutions based on incremental algorithms will become more important to address the problems with the costly computation times for streaming, over-time datasets. Incremental algorithms can benefit from early pruning by updating the affected parts only when an incremental update is made in the network. This paper provides an example of this case by demonstrating the design of an incremental closeness centrality algorithm that supports efficient computation of allpairs of shortest paths and closeness centrality in dynamic social networks that are continuously updated by addition, removal, and modification of nodes and edges. Our results obtained on various synthetic and real-life datasets provide significant speedups over the most commonly used way of computing closeness centrality, suggesting that incremental algorithm design is a fruitful research area for social network analysts.

Procedia Computer Science, 2013

Betweenness centrality is a graph analytic that states the importance of a vertex based on the number of shortest paths that it is on. As such, betweenness centrality is a building block for graph analysis tools and is used by many applications, including finding bottlenecks in communication networks and community detection. Computing betweenness centrality is computationally demanding, O(V 2 + V · E) (for the best known algorithm), which motivates the use of parallelism. Parallelism is especially needed for large graphs with millions of vertices and billions of edges. While the the memory requirements for computing betweenness are not as demanding, O(V + E) (for the best known sequential algorithm), these bound increase for different parallel algorithms. We show that is possible to reduce the memory requirements for computing betweenness centrality from O(V + E) to O(V) at the expense of doing additional traversals. We show that not only does this not hurt performance it actually improves performance for coarse grain parallelism. Further, we show that using the new approach allows parallel scaling that previously was not possible. One example is that the new approach is able to scale to 40 x86 cores for a graph with 32M vertices and 2B edges, whereas the previous approach is only able to scale upto 6 cores because of memory requirements. We also do analysis of fine-grain parallel betweenness centrality on both the x86 and the Cray XMT.

2017

Betweenness centrality is a widely adopted metric to analyze the impact of critical nodes of graphs in several domains (social, biological, transportation, service, computer networks). Its exact computation is very demanding due to an O(nm) time complexity on a graph with n nodes and m edges. This represents an obstacle to the adoption of betweenness centrality for continuous monitoring of critical nodes in very large networks. In this paper, we analyze the performance of a parametric two-level clustering algorithm for computing approximated values of betweenness with different kinds of graph. The analysis aims at evaluating how the properties of different complex networks impact the reduction of the number of single-source shortest-paths explorations of Brandes’ algorithm. The results confirm that one-level clustering strongly reduces the number of pivots (and consequently the computation time) on scale-free graphs, while small-world (and random) graphs need an additional level of ...