Delta-Screening: A Fast and Efficient Technique to Update Communities in Dynamic Graphs

Abstract

Detecting communities in time-evolving/dynamic networks is an important operation used in many real-world network science applications. While there have been several proposed strategies for dynamic community detection, such approaches do not necessarily take advantage of the locality of changes. In this paper, we present a new technique called Delta-Screening (or simply, ∆-screening) for updating communities in a dynamic graph. The technique assumes that the graph is given as a series of time steps, and outputs a set of communities for each time step. At the start of each time step, the ∆-screening technique examines all changes (edge additions and deletions) and computes a subset of vertices that are likely to be impacted by the change (using the modularity objective). Subsequently, only the identified subsets are processed for community state updates. Our experiments demonstrate that this scheme, despite its ability to prune vertices aggressively, is able to generate significant savings in runtime performance (up to 38× speedup over static baseline and 5× over dynamic baseline implementations), without compromising on the quality. We test on both real-world and synthetic network inputs containing both edge additions and deletions. The ∆-screening technique is generic to be incorporated into any of the existing modularity-optimizing clustering algorithms. We tested using two state-of-the-art clustering implementations, namely, Louvain and SLM. In addition, we also show how to use the ∆-screening approach to delineate appropriate intervals of temporal resolutions at which to analyze a given input network.

Dynamic Community Detection Decouples Multiple Time Scale Behavior of Complex Chemical Systems

“…The Δ-screening algorithm internally identifies a subset of vertices (denoted by scriptR t ) and updates the community assignments only for those nodes in that subset. The details of the selection procedure, as well as related properties and experimental analysis of the algorithm, are provided in Zarayeneh and Kalyanaraman . After this procedure is completed for all T timesteps, the final output is a time series of community sets: { C 1 , C 2 , ··· C T } .…”

“…The cost of detecting communities at the first timestep is proportional to the size of the network scriptO ( ( false| V 1 | + false| E 1 | ) × r false) , where r denotes the number of iterations the Louvain algorithm takes to converge (input dependent and typically a constant in tens or at most hundreds on most practical inputs , ). For each subsequent timestep t , the Δ-screening method , takes scriptO false( f t ( false| V 1 | + false| E 1 | ) × r t ) , where f t ∈ [0, 1] denotes the fraction of the input graph selected by the Δ-screening procedure and k t denotes the number of iterations taken to converge on that reduced graph. Intuitively, Δ-screening selects subgraphs to run Louvain based on where the changes appear, and the fractional value f t is proportional to the sizes of the communities impacted by those changes.…”

“…Step 1: Incremental Community Detection at Timestep t. The communities at any given timestep t are detected using the Δ-screening algorithm, 46 which employs the Louvain algorithm 49 internally to assign communities to nodes. Importantly, Δ-screening only uses Louvain on a selected subset of nodes that are likely to be impacted by edge additions and/or deletions that occur between time t to t + 1.…”

“…, where r denotes the number of iterations the Louvain algorithm takes to converge (input dependent and typically a constant in tens or at most hundreds on most practical inputs 49,51 ). For each subsequent timestep t, the Δscreening method 46,52 takes…”

“…34−45 These incremental approaches have the advantage of generating more stable communities over time, thereby facilitating an easier tracking of the evolution of communities. The Δ-screening method 46 is an incremental approach where, at each timestep, a subset of nodes in the network is identified that are expected to be impacted by node or edge additions and deletions that occur in the fluctuating network. Computation of any potential community change is then restricted to only that subset of nodes.…”