Generative model for feedback networks

• DOI: 10.1103/physreve.73.016119
• Publication Date: 2006-01-23T19:41:29Z
• Authors: Douglas R. White; Nataša Kejžar; Constantino Tsallis; Doyne Farmer; Scott White
• Keywords: Statistical Mechanics (cond-mat.stat-mech); FOS: Physical sciences; feedback; Disordered Systems and Neural Networks (cond-mat.dis-nn); Condensed Matter - Disordered Systems and Neural Networks; simulation; nonextensive entropy; 01 natural sciences; Social networks; q-exponential; 0103 physical sciences; generatibve model; Condensed Matter - Statistical Mechanics

We investigate a simple generative model for network formation. The model is designed to describe the growth of networks of kinship, trading, corporate alliances, or autocatalytic chemical reactions, where feedback is an essential element of network growth. The underlying graphs in these situations grow via a competition between cycle formation and node addition. After choosing a given node, a search is made for another node at a suitable distance. If such a node is found, a link is added connecting this to the original node, and increasing the number of cycles in the graph; if such a node cannot be found, a new node is added, which is linked to the original node. We simulate this algorithm and find that we cannot reject the hypothesis that the empirical degree distribution is a q-exponential function, which has been used to model long-range processes in nonequilibrium statistical mechanics.<br/>11 pages, 6 figures<br/>