Closeness centrality is one way of measuring how central a node is in the given network. The closeness centrality measure assigns a centrality value to each node based on its accessibility to the whole network. In real life applications, we are mainly interested in ranking nodes based on their centrality values. The classical method to compute the rank of a node first computes the closeness centrality of all nodes and then compares them to get its rank. Its time complexity is @math , where @math represents total number of nodes, and @math represents total number of edges in the network. In the present work, we propose a heuristic method to fast estimate the closeness rank of a node in @math time complexity, where @math . We also propose an extended improved method using uniform sampling technique. This method better estimates the rank and it has the time complexity @math , where @math . This is an excellent improvement over the classical centrality ranking method. The efficiency of the proposed methods is verified on real world scale-free social networks using absolute and weighted error functions.
Most of the real life applications focus on identifying few top nodes having the highest closeness centrality. proposed a method to rank @math highest closeness centrality nodes using a hybrid of approximate and exact algorithms @cite_39 . Ufimtsev proposed an algorithm to identify high closeness centrality nodes using group testing @cite_0 . presented an efficient technique to find @math most central nodes based on closeness centrality @cite_14 . They used intermediate results of centrality computation to minimize the computation time. proposed a faster method to identify top- @math nodes in undirected networks by approximating the upper bound on closeness centrality using BFT @cite_5 .
@cite_0 @cite_5 @cite_14 @cite_39
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Centrality metrics have shown to be highly correlated with the importance and loads of the nodes within the network traffic. In this work, we provide fast incremental algorithms for closeness centrality computation. Our algorithms efficiently compute the closeness centrality values upon changes in network topology, i.e., edge insertions and deletions. We show that the proposed techniques are efficient on many real-life networks, especially on small-world networks, which have a small diameter and spike-shaped shortest distance distribution. We experimentally validate the efficiency of our algorithms on large-scale networks and show that they can update the closeness centrality values of 1.2 million authors in the temporal DBLP-coauthorship network 460 times faster than it would take to recompute them from scratch. Analyzing networks requires complex algorithms to extract meaningful information. Centrality metrics have shown to be correlated with the importance and loads of the nodes in network traffic. Here, we are interested in the problem of centrality-based network management. The problem has many applications such as verifying the robustness of the networks and controlling or improving the entity dissemination. It can be defined as finding a small set of topological network modifications which yield a desired closeness centrality configuration. As a fundamental building block to tackle that problem, we propose incremental algorithms which efficiently update the closeness centrality values upon changes in network topology, i.e., edge insertions and deletions. Our algorithms are proven to be efficient on many real-life networks, especially on small-world networks, which have a small diameter and a spike-shaped shortest distance distribution. In addition to closeness centrality, they can also be a great arsenal for the shortest-path-based management and analysis of the networks. We experimentally validate the efficiency of our algorithms on large networks and show that they update the closeness centrality values of the temporal DBLP-coauthorship network of 1.2 million users 460 times faster than it would take to compute them from scratch. To the best of our knowledge, this is the first work which can yield practical large-scale network management based on closeness centrality values. The significance of an entity in a network is generally given by the centrality value of its vertex. For most analysis purposes, only the high ranked vertices are required. However, most algorithms calculate the centrality values of all the vertices. We present an extremely fast and scalable algorithm for identifying the high closeness centrality vertices, using group testing. We show that our approach is significantly faster (best-case over 50 times, worst-case over 7 times) than the currently used methods. We can also use group testing to identify networks that are sensitive to edge perturbation. Given a social network, which of its nodes are more central? This question has been asked many times in sociology, psychology and computer science, and a whole plethora of centrality measures (a.k.a. centrality indices, or rankings) were proposed to account for the importance of the nodes of a network. In this paper, we approach the problem of computing geometric centralities, such as closeness [1] and harmonic centrality [2], on very large graphs; traditionally this task requires an all-pairs shortest-path computation in the exact case, or a number of breadth-first traversals for approximated computations, but these techniques yield very weak statistical guarantees on highly disconnected graphs. We rather assume that the graph is accessed in a semi-streaming fashion, that is, that adjacency lists are scanned almost sequentially, and that a very small amount of memory (in the order of a dozen bytes) per node is available in core memory. We leverage the newly discovered algorithms based on HyperLogLog counters [3], making it possible to approximate a number of geometric centralities at a very high speed and with high accuracy. While the application of similar algorithms for the approximation of closeness was attempted in the MapReduce [4] framework [5], our exploitation of HyperLogLog counters reduces exponentially the memory footprint, paving the way for in-core processing of networks with a hundred billion nodes using "just" 2TiB of RAM. Moreover, the computations we describe are inherently parallelizable, and scale linearly with the number of available cores.