Statistical mechanics of complex networks
Statistical mechanics of complex networks
Networks: An Introduction
Scalable analysis for large social networks: the data-aware mean-field approach
SocInfo'12 Proceedings of the 4th international conference on Social Informatics
Toward a next generation of network models for the web
Proceedings of the 5th Annual ACM Web Science Conference
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We investigate the general conditions under which power laws emerge in networks for the degree distributions (the number of links a node has). Our study is based on a new and versatile random-walk network model (the exciton model) that includes all processes of link creation, link removal, node creation and node loss. From the principle of detailed balance simple 'litmus' test criteria for the emergence of power laws are derived. Results are compared with existing models in the network science literature, and we show how they can be generalized. An important result is that there is a very broad set of conditions under which power laws will emerge, among them nonlinearity in network formation. We show that power laws may be explained purely as a mesoscopic statistical phenomenon, on the basis of the scale-free network statistics assumption of equiprobability of existing nodes plus links. Hence, explanations rooted in making (microscopic) assumptions about individual preferences or behaviour can be avoided. The causal mechanism underlying this scale-free network statistics is, we suggest, the social and self-reinforcing mechanism of information feedback to network actors about structure and status of the network itself.