Transitivity of reciprocal networks

Network models are a useful tool to describe and predict dynamic relationships in large collections of data. Characterizing these relationships helps us to explain the emergence of structure as a systematic deviation from random connectivity. This paper introduces an event-driven model that captures the effects of three simple network formation mechanisms: random attachment (a generic abstraction of how a new incoming node connects to a network), triad formation (how the new node establishes transitive relationships), and network response (the way the overall network reacts to attachments). Our work focuses on the impact of the latter on clustering and degree distributions. We prove that any initial network will reach stationary local clustering coefficients, and obey an extended power law distribution for the in-degree and an exponential distribution for the out-degree. For the in-degree in particular, the response mechanism amplifies the scaling behavior that results from the other two mechanisms.