Optimal timescale for community detection in growing networks

Abstract

Time-stamped data are increasingly available for many social, economic, and information systems that can be represented as networks growing with time. The World Wide Web, social contact networks, and citation networks of scientific papers and online news articles, for example, are of this kind. Static methods can be inadequate for the analysis of growing networks as they miss essential information on the system's dynamics. At the same time, time-aware methods require the choice of an observation timescale, yet we lack principled ways to determine it. We focus on the popular community detection problem which aims to partition a network's nodes into meaningful groups. We use a multi-layer quality function to show, on both synthetic and real datasets, that the observation timescale that leads to optimal communities is tightly related to the system's intrinsic aging timescale that can be inferred from the time-stamped network data. The use of temporal information leads to drastically different conclusions on the community structure of real information networks, which challenges the current understanding of the large-scale organization of growing networks. Our findings indicate that before attempting to assess structural patterns of evolving networks, it is vital to uncover the timescales of the dynamical processes that generated them.A popular approach to community detection is to maximize a function, called modularity, which quantifies how much the total number of intra-community edges deviates from its expected value under a null model that preserves the individual nodes' number of connections [24]. Modularity has been studied from many viewpoints, and it is widely-recognized as a standard tool in network analysis [18]. Despite past research and the wide use of modularity optimization in a broad range of contexts, we still lack a systematic understanding of its behavior and performance in growing networks where time and aging phenomena are fundamental [25][26][27]. Albeit modularity has been used in such systems in its original form [28][29][30], the results can be expected to be suboptimal as modularity neglects the vital time information. A multi-layer form of modularity has been developed that can take into account network snapshots at various times [31,32]. However, when we wish to apply a multi-layer approach to identify relevant communities in growing networks, we face an impasse: existing works assume layered input data [31][32][33][34] and thus they do not consider the question of how to divide an arbitrary time-stamped network into layers. Addressing this question requires to choose an appropriate observation timescale, i.e. the temporal duration for each layer [5,35,36]. This choice is essential because different timescales might reveal substantially different community structures, which in turn might lead to different conclusions on the large-scale organization of the system.In this work, we derive analytically a criterion to estimate when a time-aggregated, static view of a growing network ceases to be ...

Finding proper time intervals for dynamic network extraction

“…However, time interval selection is still an open subject. It directly affects the dynamics of simulated epidemics and information spread, mixing properties of random walk, synchronization on networks [9], and various analysis such as community detection [10,11], link prediction, attribute prediction, and change-point detection [12]. Recently, several studies are dedicated to find proper time intervals [10][11][12][13][14][15][16][17].…”

“…It directly affects the dynamics of simulated epidemics and information spread, mixing properties of random walk, synchronization on networks [9], and various analysis such as community detection [10,11], link prediction, attribute prediction, and change-point detection [12]. Recently, several studies are dedicated to find proper time intervals [10][11][12][13][14][15][16][17]. It is widely accepted that the system's time span should be divided into time intervals that are neither small enough to make the network noisy nor large enough to ignore significant time-dependent effects on the network [15,18,19].…”

Knowledge evolution : from the complex network perspective

“…In general, if we set one time step too long, we will lose a lot of detail; if we set one time step too short, the fluctuation may overwhelm the real signal. Recent research suggested that the timescale may also affect community detection [Medo et al, 2018]. To balance these effects, we choose one year as one time step, while the optimal choice of timescale remains an open question.…”