2017/22 LEM Working Paper Series

Complexity and Heterogeneity in a Dynamic Network

David Lambert and Fabio Vanni
Complexity, heterogeneity, critical phenomena, network value, coordination costs, stochastic processes

  JEL Classifications
D85, C02, C22, C62

We present an analytical solution for the connectivity of a network model with a ”non-simultaneous” linking scheme. Despite its simplicity, this model exhibits node-space correlations in the link distribution, and anomalous fluctuations behavior of the time series of the connectivity variable, and a finite-size e ff ect: the maximum number of links occurs away from the critical value of the system parameter. We derive an exact Master Equation for this model using a quantum algebra approach to stochastic processes. Fluctuations are much more important than the mean-field approximation predicts, which we attribute to the heterogeneity in the model. The maximal heterogeneous population corresponds to the critical value of the system. Finally as an explanatory case we evaluate the growth of the network value in relation with the system interconnectedness.
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