Modelling the Emergence of Communities in Weighted Social Networks

Over the years network theory has proven to be very versatile and
rapidly expanding methodology to investigate various complex systems,
turning out
recently to give quite unparalleled insight to their structure,
function, and
response through data analysis, modeling, and simulation. For social
systems in
particular the network approach has empirically revealed a modular
structure due
to interplay between the network topology and link weights/tie strengths
between
nodes/individuals. This inspired us to develop a simple network model
that could
catch some salient features of mesoscopic community and macroscopic
topology
formation during network evolution. Our model is based on two fundamental
mechanisms of network sociology for an individual to find new friends,
namely {it cyclic closure} and {it focal closure}, which are mimicked
by local
search-link-reinforcement and random global attachment mechanisms. In
addition the
model includes node deletion mechanism with its links simultaneously
removed, which
corresponds for an individual to depart from the network. Our model
turned out to
produce many features of the empirically studied large social network,
and could possibly be used for studying various collective social
phenomena such
as spreading, formation, and evolutionary processes.