Simulating the Dynamics of Scale-Free Networks via Optimization

Abstract

We deal here with the issue of complex network evolution. The analysis of topological evolution of complex networks plays a crucial role in predicting their future. While an impressive amount of work has been done on the issue, very little attention has been so far devoted to the investigation of how information theory quantifiers can be applied to characterize networks evolution. With the objective of dynamically capture the topological changes of a network's evolution, we propose a model able to quantify and reproduce several characteristics of a given network, by using the square root of the Jensen-Shannon divergence in combination with the mean degree and the clustering coefficient. To support our hypothesis, we test the model by copying the evolution of well-known models and real systems. The results show that the methodology was able to mimic the test-networks. By using this copycat model, the user is able to analyze the networks behavior over time, and also to conjecture about the main drivers of its evolution, also providing a framework to predict its evolution.

Quantification of network structural dissimilarities

“…Similarity measures have many uses due to the current widespread use of networks in social sciences, medicine, biology, physics and so on192021222324252627282930. They can help, among many other examples, to discriminate between neurological disorders by quantifying functional and topological similarities31, to find structurally more similar molecules that are more likely to exhibit similar properties, for drug design32, and to quantify changes in temporal evolving networks22.…”

Information theory perspective on network robustness

“…In this work, we propose a measure for network robustness based on the Jensen-Shannon divergence, an Information Theory quantifier that already showed to be very effective in measuring small topological changes in a network (Carpi et al, 2011;Schieber and Ravetti, 2013;Schieber et al, 2014). This method considers failures occurring in a temporal sequence capturing, in some sense, the dynamics of the role of the remaining links after each single failure.…”