The Parameterized Complexity of Centrality Improvement in Networks

TL;DR

This paper investigates the computational complexity of increasing a vertex's centrality in networks by adding edges, revealing hardness results but also identifying specific cases where the problem is tractable.

Contribution

It provides a detailed parameterized complexity analysis of centrality improvement problems, including hardness results and a tractability result for certain graph classes.

Findings

Hardness results for the natural parameter in general cases

Identification of tractability when vertex deletion distance to cluster graphs is small

Analysis of closeness and betweenness centrality improvement problems

Abstract

The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact on the network or less transportation or administration cost. In this work we study the parameterized complexity of the NP-complete problems Closeness Improvement and Betweenness Improvement in which we ask to improve a given vertex' closeness or betweenness centrality by a given amount through adding a given number of edges to the network. Herein, the closeness of a vertex v sums the multiplicative inverses of distances of other vertices to v and the betweenness sums for each pair of vertices the fraction of shortest paths going through v. Unfortunately, for the natural parameter "number of edges to add" we obtain hardness results, even in rather restricted cases. On the positive side, we also give an island of tractability for the parameter measuring the vertex deletion distance to cluster graphs.