Stability and Similarity in Networks Based on Topology and Nodes Importance

Abstract

We propose a model that evaluates how much a network has changed over time in terms of its structure and a set of central elements. The difference of structure is evaluated in terms of node-to-node influence using known nodes correspondence models. To analyze the changes in nodes centralities we adapt an idea of interval orders to the network theory. Our approach can be used to investigate dynamic changes in temporal networks and to identify suspicious or abnormal effects in terms of the topology and its critical members. We can also transform the stability measure to the similarity measure in order to cluster the network in some homogeneous periods. To test our model, we consider the international migration network from 1970 to 2015 and attempt to analyze main changes in migration patterns.