2017/22  LEM Working Paper Series  
Complexity and Heterogeneity in a Dynamic Network 

David Lambert and Fabio Vanni 

Keywords  
Complexity, heterogeneity, critical phenomena, network value, coordination costs, stochastic processes


JEL Classifications  
D85, C02, C22, C62


Abstract  
We present an analytical solution for the connectivity of a network
model with a ”nonsimultaneous” linking scheme. Despite its
simplicity, this model exhibits nodespace correlations in the link
distribution, and anomalous fluctuations behavior of the time series
of the connectivity variable, and a finitesize 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 meanfield 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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