Accelerating Computation of Distance Based Centrality Measures for Spatial Networks

In this paper, by focusing on spatial networks embedded in the real space, we first extend the conventional step-based closeness and betweenness centralities by incorporating inter-nodes link distances obtained from the positions of nodes. Then, we propose a method for accelerating computation of these centrality measures by pruning some nodes and links based on the cut links of a given spatial network. In our experiments using spatial networks constructed from urban streets of cities of several types, our proposed method achieved about twice the computational efficiency compared with the baseline method. Actual amount of reduction in computation time depends on network structures. We further experimentally show by examining the highly ranked nodes that the closeness and betweenness centralities have completely different characteristics to each other.

[1]  Alexandre M. Bayen,et al.  Understanding Road Usage Patterns in Urban Areas , 2012, Scientific Reports.

[2]  Alper Yilmaz,et al.  A SOCIAL NETWORK ANALYSIS APPROACH TO ANALYZE ROAD NETWORKS , 2010 .

[3]  Masahiro Kimura,et al.  Resampling-Based Framework for Estimating Node Centrality of Large Social Network , 2014, Discovery Science.

[4]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[5]  Jon M. Kleinberg,et al.  Mining the Web's Link Structure , 1999, Computer.

[6]  Edith Cohen,et al.  Sketch-based Influence Maximization and Computation: Scaling up with Guarantees , 2014, CIKM.

[7]  Alessandro Vespignani,et al.  The Structure of Interurban Traffic: A Weighted Network Analysis , 2005, physics/0507106.

[8]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[9]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[10]  Kerstin Burckhart,et al.  An Interpretation of the Recent Evolution of the City of Barcelona through the Traffic Maps , 2012 .

[11]  Sebastiano Vigna,et al.  In-Core Computation of Geometric Centralities with HyperBall: A Hundred Billion Nodes and Beyond , 2013, 2013 IEEE 13th International Conference on Data Mining Workshops.

[12]  Silvio Lattanzi,et al.  Efficient Algorithms for Public-Private Social Networks , 2015, KDD.

[13]  Edith Cohen,et al.  All-Distances Sketches, Revisited: HIP Estimators for Massive Graphs Analysis , 2013, IEEE Transactions on Knowledge and Data Engineering.

[14]  Edith Cohen,et al.  Size-Estimation Framework with Applications to Transitive Closure and Reachability , 1997, J. Comput. Syst. Sci..

[15]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[16]  Masahiro Kimura,et al.  Super mediator - A new centrality measure of node importance for information diffusion over social network , 2016, Inf. Sci..

[17]  V. Latora,et al.  Centrality measures in spatial networks of urban streets. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  John Skvoretz,et al.  Node centrality in weighted networks: Generalizing degree and shortest paths , 2010, Soc. Networks.

[19]  Masahiro Kimura,et al.  Speeding-up node influence computation for huge social networks , 2015, International Journal of Data Science and Analytics.

[20]  H. Moritz,et al.  Geodetic reference system 1980 , 1988 .