Detecting sequences of system states in temporal networks

Abstract

Many time-evolving systems in nature, society and technology leave traces of the interactions within them. These interactions form temporal networks that reflect the states of the systems. In this work, we pursue a coarse-grained description of these systems by proposing a method to assign discrete states to the systems and inferring the sequence of such states from the data. Such states could, for example, correspond to a mental state (as inferred from neuroimaging data) or the operational state of an organization (as inferred by interpersonal communication). Our method combines a graph distance measure and hierarchical clustering. Using several empirical data sets of social temporal networks, we show that our method is capable of inferring the system’s states such as distinct activities in a school and a weekday state as opposed to a weekend state. We expect the methods to be equally useful in other settings such as temporally varying protein interactions, ecological interspecific interactions, functional connectivity in the brain and adaptive social networks.

Structure and function in human and primate social networks: implications for diffusion, network stability and health

“…Other factors that might cause networks to restructure themselves include a reduction in the time available for social interaction, access to a sufficiently large population to allow choice [128] or a change in the proportion of phenotypes (sex, personality or family size) when these behave differently. Methods for studying networks that change dynamically through time have been developed [142], although in practice these typically reflect past change rather than how networks are likely to respond to future challenges. Here, my concern is with how networks might change as a consequence of the internal and external forces acting on them.…”

Community-based time segmentation from network snapshots

“…A very similar approach is given by Masuda and Holme, who use hierarchical clustering to label slices as "states" of the system, which are expected to recur (Masuda and Holme 2019). Their work differs from ours in two major ways.…”

Unsupervised network embeddings with node identity awareness

“…On the other hand, the spectral distances for graphs have proven to be very useful in many applications (Masuda and Holme 2019;Wilson and Zhu 2008). However, the spectral nature of the method makes it invariant to node permutations.…”

“…For any L and L we consider the following spectral distance. The spectral distance between two undirected graphs G 1 and G 2 is defined as Masuda and Holme (2019):…”