Elementary models of dynamic networks

Abstract

Inspecting the dynamics of networks opens a new dimension in understanding the interactions among the components of complex systems. Our goal is to understand the baseline properties expected from elementary random changes over time, in order to be able to assess the various effects found in longitudinal data. We created elementary dynamic models from classic random and preferential networks. Focusing on edge dynamics, we defined several processes for changing networks of a fixed size. We applied simple rules, including random, preferential and assortative modifications of existing edges – or a combination of these. Starting from initial Erdos-Renyi networks, we examined various basic network properties (e.g., density, clustering, average path length, number of components, degree distribution, etc.) of both snapshot and cumulative networks (for various lengths of aggregation time windows). Our results provide a baseline for changes to be expected in dynamic networks. We found universalities in the dynamic behavior of most network statistics. Furthermore, our findings suggest that certain network properties have a strong, non-trivial dependence on the length of the sampling window.