Physica A 377 (2007) 698–708 A Monte Carlo model for networks between professionals and society Henning Frydenlund Hansen à , Alex Hansen Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Received 13 September 2006; received in revised form 6 November 2006 Available online 15 December 2006 Abstract We propose a network model with a fixed number of nodes and links and with a dynamic which favors links between nodes differing in connectivity. We observe a phase transition and parameter regimes with degree distributions following power laws, PðkÞk g , with g ranging from 0:2 to 0:5, small-world properties, with a network diameter following DðNÞ log N and relative high clustering, following CðNÞ1=N and CðkÞk a , with a close to 3. We compare our results with data from real-world protein interaction networks. r 2006 Elsevier B.V. All rights reserved. Keywords: Protein networks; Social systems; Network model 1. Introduction Over the last few years a large number of network models have been put forward, highly motivated by empirical studies of real-world networks [1]. The various models can be categorized belonging to one of the three main classes of modeling paradigms. First, different variants of the random graph model of Erd + os and Re´nyi [2] are still used for comparison with many different models and empirical studies [3]. The second group of network models are referred to as small- world models, first presented by Watts and Strogatz [4] and are motivated by high clustering observed in many real-world networks. This group of network models aims to include both the idea of highly clustered networks and random graphs. Third, the construction of various scale-free models have been motivated by the discovering of power-law degree distributions in real-world networks, ranging from the World Wide Web [5] to the network of Science collaboration [6] and the web of human sexual contacts [7]. This group of network models focuses on the dynamics of the network and aims to offer a universal theory of network evolution [3]. In the past few years, a wide range of concepts and measures for complex networks have been proposed and investigated. However, complex networks are most often described by three basic concepts. The small-world concept describes the fact that there is a relative short path between any two nodes in most networks. The maximum of the shortest paths between any two nodes, referred to as the diameter, is often ARTICLE IN PRESS www.elsevier.com/locate/physa 0378-4371/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2006.11.064 à Corresponding author. E-mail addresses: Henning.Hansen@ntnu.no (H.F. Hansen), Alex.Hansen@ntnu.no (A. Hansen).