Temporal local clustering coefficient uncovers the hidden pattern in temporal networks

Identifying and extracting topological characteristics are essential for understanding associated structures and organizational principles of complex networks. For temporal networks where the network topology varies with time, beyond the classical patterns such as small-worldness and scale-freeness extracted from the perspective of traditional aggregated static networks, the temporality and simultaneity of time-varying interactions should also be included. Here we extend the traditional analysis on the local clustering coefficient $C$ in static networks and study the dynamical local clustering coefficient of temporal networks. We demonstrate that the temporal local clustering coefficient $TC$ conveys the hidden information of nodes' neighboring connectance when interactions occur at various rhythms. By systematically analyzing various empirical datasets, we find that $TC$ uncovers different interaction patterns in different types of temporal networks. Specifically, we show that $TC$ has a strong positive correlation with $C$ in efficiency-related networks, whereas they are uncorrelated in social activity-related networks. Moreover, $TC$ helps to exclude interference from accidental interactions and reflect the actual clustering properties of network nodes. Our results shed light on the importance of digging into dynamical characteristics to fundamentally understand the underlying temporal structures of real complex systems.