Current Flow Group Closeness Centrality for Complex Networks

02/07/2018
by   Huan Li, et al.
0

Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend the notion of CFCC to a group of vertices in a weighted graph. For a graph with n vertices and m edges, the CFCC C(S) for a vertex group S is equal to the ratio of n to the sum of effective resistances from S to all other vertices. We then study the problem of finding a group S^* of k vertices, so that the CFCC C(S^*) is maximized. We alternatively solve this problem by minimizing the reciprocal of C(S^*). We show that the problem is NP-hard, and prove that the objective function is monotone and supermodular. We propose two greedy algorithms with provable approximation guarantees. The first is a deterministic algorithm with an approximation factor (1-1/e) and O(n^3) running time; while the second is a randomized algorithm with a (1-1/e-ϵ)-approximation and O (k mϵ^-2) running time for any small ϵ>0, where the O (·) notation hides the poly factors. Extensive experiments on models and real networks demonstrate that our algorithms are effective and efficient, with the second algorithm being scalable to massive networks with more than a million vertices.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/03/2021

Deterministic Min-cut in Poly-logarithmic Max-flows

We give a deterministic algorithm for finding the minimum (weight) cut o...
research
07/05/2021

Spanner Approximations in Practice

A multiplicative α-spanner H is a subgraph of G=(V,E) with the same vert...
research
06/07/2021

Local Algorithms for Estimating Effective Resistance

Effective resistance is an important metric that measures the similarity...
research
10/30/2019

Group Centrality Maximization for Large-scale Graphs

The study of vertex centrality measures is a key aspect of network analy...
research
08/14/2023

Minimizing Polarization in Noisy Leader-Follower Opinion Dynamics

The operation of creating edges has been widely applied to optimize rele...
research
01/15/2021

New Approximation Algorithms for Forest Closeness Centrality – for Individual Vertices and Vertex Groups

The emergence of massive graph data sets requires fast mining algorithms...
research
04/18/2018

Improving information centrality of a node in complex networks by adding edges

The problem of increasing the centrality of a network node arises in man...

Please sign up or login with your details

Forgot password? Click here to reset