Convergence of Random to Power-Law Networks Using a Multi-objective Non-linear Programming Model

Networks are a powerful and useful tool for analysing complex systems. Three main types of networks have been proposed in the relative literature in order to interpret adequately evolving or stationary phenomena. In this research, two network structures are analysed; the first type is the random network, which was initially introduced by Erdos and Rényi. Random networks properties remain the same over time, and they do not exhibit high degree of clustering, whereas the second structure studied, the power‐law network that have been examined by Albert and Barabási, can incorporate attributes that are observed in natural networks (i.e. the World Wide Web and the authors' collaboration). In this study, an attempt is made to investigate the conditions under which random network and power law (or scale free) converge into one at a given time point. Three main metrics are used in order to examine the proximity between the studied structures: (i) clustering coefficient, (ii) average path length and (iii) degree distribution. Considering the difference of the corresponding metrics of each network type as an objective function, a multi‐objective discontinuous non‐linear programming model is employed using the weighted sum model as a solution approach. A statistical meta‐analysis is performed using a multivariate logit model in order to assess the effect of each network's specific variables on the objective function.