Analysis of Network Topology Using the Threshold-Minimum Dominating Set

Abstract

Graph theory is an essential tool for the modeling of complex networks. It can be used for network control and monitoring. The latter is usually performed using a representative subset of the whole network identified with the Minimum Spanning Tree (MST) methodology. The MST, however, bears intrinsic limitations since it may lead to the formation of an inappropriate set of nodes that may withhold crucial information. In this study we unveil these limitations and propose the use of a novel methodology, the Threshold-Minimum Dominating Set (T-MDS), to derive a minimum subset of nodes that can adequately and efficiently describe the collective behavior of an entire network. We present two diverse empirical examples regarding a) a banking network of 200 U.S. banks and b) the GDP growth rates based network of 22 European countries to illustrate the advantages of the T-MDS methodology in the analysis of complex economic systems.

Keywords: Networks, Graph Theory, Optimization, Threshold-Minimum Dominating Set, Minimum Spanning Tree, Bank Supervision