2017/16 | LEM Working Paper Series | ||||||||||||||||
Time evolution of an agent-driven network model |
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Fabio Vanni and Paolo Barucca |
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Keywords | |||||||||||||||||
Network formation,temporal evolution, stochastic process, financial networks, critical transitions
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JEL Classifications | |||||||||||||||||
D85, C62, G21
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Abstract | |||||||||||||||||
We present a new approach to the study of networks where the formation
of links is driven by unilateral initiative of nodes. First, we
propose a mathematical description of the extreme introvert and
extrovert model (XIE), a dynamic network model in which the number of
links fluctuates over time according to the degree-preferences of
nodes. Second, we introduce a generalization of the model in which
intermittent states can make the evolution of connectivity slower. In
this class of networks, system evolution has nodes which can either
create or destroy links according to their target attitudes. This
model belongs to a class of networks not based on the rationale of
linking probability between pair of nodes, but it is based on the
initiative of the single units when they act. We select the minimal
case of a bipartite network where we have two groups of nodes, each
group has nodes with a given capability to bear links. One group
(high-target) is composed by nodes that create as many links as
possible, the extroverts. The other group (low-target) is composed by
nodes that delete as many links as possible, i.e. the introverts. We
here provide a novel analytical formulation of the system evolution
through coupled Master Equations for the two interacting populations,
recovering the steady state degree distributions and a new analytical
description of the transient dynamics to the equilibrium. Moreover, we
provide numerical evidence supporting the existence of an extreme
Thouless effect in this model, i.e. a mixed-phase transition at which
the order parameter, here given by the network connectivity, displays
a discontinuous jump and large dynamic fluctuations. Fluctuations are
also shown to be connected to a peak in degree correlation at the
transition, corresponding to same size populations of extroverts and
introverts.
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