The Spatially-Weighted Temporal Rich Club: Identifying Rich Clubs in Spatiotemporal Interaction Networks

Abstract

In network science, the rich club phenomenon describes the propensity of 'rich' nodes—typically high-degree nodes—to create densely interconnected sub-networks. Various definitions of the rich club exist, ranging from the density of edge connections to the summation of edge weights associated with rich club nodes. Meanwhile, other works have focused on evaluating the significance of detected rich club coefficients using null models. While the analysis of topological and weighted rich clubs predominantly occurs in static networks, there is a growing body of research exploring the temporal dimensions of these networks. Specifically, the Temporal Rich Club (TRC) coefficient, as defined by Pedreschi et al. (2022), quantifies the extent to which high-degree nodes connect in a stable and concurrent manner. Since this method relies on edge connections rather than weights, it could also be termed the Topological Temporal Rich Club (TTRC). Being topologically-defined, this method may not detect temporal rich clubs present in networks in which the nodes have similar degrees but vastly different weighted degrees, such as in many spatiotemporal human mobility flow networks. To address this gap, we introduce the Weighted Temporal Rich Club (WTRC). Building on the work of Alstott et al. (2014), we propose simplified calculations for both TTRC and WTRC, ensuring the use of appropriate null models. This allows for a clear distinction between topological and weighted rich club effects and enables the assessment of the rich club phenomenon's significance. Overall, this research enhances network analysis by facilitating the detection of rich clubs across various temporal network types.