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.
Real world networks are highly dynamic and the computation of closeness centrality of all nodes for each change in the networks will be a cumbersome task. In dynamic networks, for each update, the closeness centrality of some nodes may remain unaffected. proposed a method to update closeness centrality in dynamic networks @cite_27 . The proposed method uses the set of affected nodes to update the closeness centrality whenever there is any addition, removal, or modification of nodes or edges. Yen also proposed an algorithm called CENDY (Closeness centrality and avErage path leNgth in DYnamic networks) to update closeness centrality whenever an edge is updated @cite_7 . proposed a method to update closeness centrality using the level difference information of breadth first traversal @cite_12 .
@cite_27 @cite_12 @cite_7
1605385825 2048468623 2963957156 2241780750
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. 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. Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on randomly sampled paths has been shown to be significantly faster in practice. However, for dynamic networks, no approximation algorithm for betweenness centrality is known that improves on static recomputation. We address this deficit by proposing two incremental approximation algorithms (for weighted and unweighted connected graphs) which provide a provable guarantee on the absolute approximation error. Processing batches of edge insertions, our algorithms yield significant speedups up to a factor of 104 compared to restarting the approximation. This is enabled by investing memory to store and efficiently update shortest paths. As a building block, we also propose an asymptotically faster algorithm for updating the SSSP problem in unweighted graphs. Our experimental study shows that our algorithms are the first to make in-memory computation of a betweenness ranking practical for million-edge semi-dynamic networks. Moreover, our results show that the accuracy is even better than the theoretical guarantees in terms of absolute errors and the rank of nodes is well preserved, in particular for those with high betweenness. Measuring the relative importance of each vertex in a network is one of the most fundamental building blocks in network analysis. Among several importance measures, betweenness centrality, in particular, plays key roles in many real applications. Considerable effort has been made for developing algorithms for static settings. However, real networks today are highly dynamic and are evolving rapidly, and scalable dynamic methods that can instantly reflect graph changes into centrality values are required. In this paper, we present the first fully dynamic method for managing betweenness centrality of all vertices in a large dynamic network. Its main data structure is the weighted hyperedge representation of shortest paths called hypergraph sketch. We carefully design dynamic update procedure with theoretical accuracy guarantee. To accelerate updates, we further propose two auxiliary data structures called two-ball index and special-purpose reachability index. Experimental results using real networks demonstrate its high scalability and efficiency. In particular, it can reflect a graph change in less than a millisecond on average for a large-scale web graph with 106M vertices and 3.7B edges, which is several orders of magnitude larger than the limits of previous dynamic methods.