On the formation of structure in growing networks

TL;DR

This paper introduces a network formation model based on triad junctions that produces networks with extended power law behavior, high clustering, and community structures, differing from traditional preferential attachment models.

Contribution

It proposes a novel mechanism for network growth emphasizing triad formation, leading to complex structural properties in directed networks.

Findings

Networks exhibit extended power law degree distributions.

High clustering and community modularity emerge naturally.

Degree distribution is mixed, with power law for high-degree nodes and exponential for others.

Abstract

Based on the formation of triad junctions, the proposed mechanism generates networks that exhibit extended rather than single power law behavior. Triad formation guarantees strong neighborhood clustering and community-level characteristics as the network size grows to infinity. The asymptotic behavior is of interest in the study of directed networks in which (i) the formation of links cannot be described according to the principle of preferential attachment; (ii) the in-degree distribution fits a power law for nodes with a high degree and an exponential form otherwise; (iii) clustering properties emerge at multiple scales and depend on both the number of links that newly added nodes establish and the probability of forming triads; and (iv) groups of nodes form modules that feature less links to the rest of the nodes.