Robust detection of dynamic community structure in networks

Abstract

We describe techniques for the robust detection of community structure in some classes of timedependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations ("optimization variance") and over randomizations of network structure ("randomization variance"). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data. Many social, physical, technological, and biological systems can be modeled as networks composed of numerous interacting parts. 1 As an increasing amount of time-resolved data has become available, it has become increasingly important to develop methods to quantify and characterize dynamic properties of temporal networks. 2 Generalizing the study of static networks, which are typically represented using graphs, to temporal networks entails the consideration of nodes (representing entities) and/or edges (representing ties between entities) that vary in time. As one considers data with more complicated structures, the appropriate network analyses must become increasingly nuanced. In the present paper, we discuss methods for algorithmic detection of dense clusters of nodes (i.e., communities) by optimizing quality functions on multilayer network representations of temporal networks. 3,4 We emphasize the development and analysis of different types of null-model networks, whose appropriateness depends on the structure of the networks one is studying as well as the construction of representative partitions that take advantage of a multilayer network framework. To illustrate our ideas, we use ensembles of time-dependent networks from the human brain and human behavior.

Dynamic network structure of interhemispheric coordination

“…Our results suggest that the extent and anatomical specificity of interhemispheric coordination is time-dependent, highlighting the usefulness of dynamic network methods to explore brain function (41,42,65). As shown in Fig.…”

“…Long interhemispheric communication is thought to be associated with low-frequency oscillatory activity (40), whereas more local processing has been linked to highfrequency activity. At an even larger scale, low-frequency brain rhythms might enable the dynamic evolution of whole-brain networks at behavioral time scales (41,42).…”

“…To identify putative functional modules in a robust, data-driven fashion and to explore their temporal evolution during the experiment, we apply recently developed dynamic community detection techniques (50)(51)(52). Following previous work (41,42,53), we constructed multilayer networks for each individual experimental condition and trial in which we link the weighted network A for each time window t to the network in the time windows before (t − 1) and after (t + 1) (Fig. 3A) by connecting each node to itself in the neighboring windows (Materials and Methods).…”

Extraction of force-chain network architecture in granular materials using community detection

“…(Such a null model was used previously for applications in neuroscience [46].) Recall that the adjacency matrix encapsulates the presence or absence of contact between each pair of particles.…”

Tracking ongoing cognition in individuals using brief, whole-brain functional connectivity patterns

“…Furthermore, FC dynamics exhibit rich spatiotemporal structure. Connections between higher order cognitive regions are more variable than those between primary sensorymotor regions (13)(14)(15), and a limited set of whole-brain, quasistable FC configurations-known as FC states-reliably recur both within and across subjects at rest (13,16).…”