Abstract
Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree. A detailed understanding if and how these scaling laws are inter-related is missing so far, let alone whether they can be understood through a common, dynamical principle. We propose a simple model for stationary network formation and show that the three mentioned scaling relations follow as natural consequences of triadic closure. The validity of the model is tested on multiplex data from a well-studied massive multiplayer online game. We find that the three scaling exponents observed in the multiplex data for the friendship, communication and trading networks can simultaneously be explained by the model. These results suggest that triadic closure could be identified as one of the fundamental dynamical principles in social multiplex network formation.
Highlights
Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree
One such local rule that is extremely relevant for social network formation is the principle of triadic closure [17, 18], which means that the probability of a new link to close a triad is higher than the probability to connect any two nodes
It is instructive to see how a combination of growth, preferential attachment and clustering processes gives rise to the three scaling laws above, this does not help us to understand if the existence and possible inter-relations of the three exponents can emerge from a single underlying dynamical origin, and to what extent this common origin is an actual feature of real social network formation processes
Summary
Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree. It is instructive to see how a combination of growth, preferential attachment and clustering processes gives rise to the three scaling laws above, this does not help us to understand if the existence and possible inter-relations of the three exponents can emerge from a single underlying dynamical origin, and to what extent this common origin is an actual feature of real social network formation processes. We study a simple model that simultaneously explains the three scaling laws in equations (1)–(3) based on the process of triadic closure in non-growing networks This process introduces a mechanism from which preferential attachment emerges, leads to fat-tailed degree distributions and induces scaling of the clustering coefficients with node degrees. The model can be fully calibrated with the multiplex data and explains three observed characteristic exponents for three different sub-networks of the multiplex
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