Dominating sets and ego-centered decompositions in social networks

TL;DR

This paper develops methods to decompose social networks into minimal ego-centered subnetworks using dominating sets, introduces heuristics for finding all minimum dominating sets, and applies these techniques to real social network data.

Contribution

It presents a heuristic approach for identifying all minimum dominating sets and introduces structural measures for comparing ego-centered decompositions in social networks.

Findings

Heuristic effectively finds all minimum dominating sets in tested networks.

Structural measures enable comparison of different ego-centered decompositions.

Application to six empirical social networks demonstrates practical utility.

Abstract

Our aim here is to address the problem of decomposing a whole network into a minimal number of ego-centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However, to find such an efficient dominating ego-centered construction, we need to be able to detect all the minimum dominating sets and to compare all the corresponding dominating ego-centered decompositions of the network. To find all the minimum dominating sets of the network, we are developing a computational heuristic, which is based on the partition of the set of nodes of a graph into three subsets, the always dominant vertices, the possible dominant vertices and the never dominant vertices, when the domination number of the network is known. To compare the ensuing dominating ego-centered decompositions of the network, we are introducing a number of structural measures that count the number of nodes and links inside and across the ego-centered subnetworks. Furthermore, we are applying the techniques of graph domination and ego=centered decomposition for six empirical social networks.