Temporal communities are the result of a consistent partitioning of nodes across multiple snapshots of an evolving network, and they provide insights into how dense clusters in a network emerge, combine, split and decay over time. To reliably detect temporal communities we need to not only find a good community partition in a given snapshot but also ensure that it bears some similarity to the partition(s) found in the previous snapshot(s), a particularly difficult task given the extreme sensitivity of community structure yielded by current methods to changes in the network structure. Here, motivated by the inertia of inter-node relationships, we present a new measure of partition distance called estrangement, and show that constraining estrangement enables one to find meaningful temporal communities at various degrees of temporal smoothness in diverse real-world datasets. Estrangement confinement thus provides a principled approach to uncovering temporal communities in evolving networks. C ommunity detection has been shown to reveal latent yet meaningful structure in networks such as groups in online and contact-based social networks, functional modules in protein-protein interaction networks, groups of customers with similar interests at online retailers, disciplinary groups of scientists in collaboration networks, etc. 1 . Temporal community detection aims to find how such communities emerge, grow, combine and decay in networks that evolve with time. Temporal communities can provide robust network-based insights into complex phenomena such as the evolution of inter-country trade networks, the emergence of celebrities in social media, the formation of distinct political ideologies, the spread of epidemics, trends in venture investment, etc. Static community detection 1 partitions a network into groups of nodes such that the intra-group edge density is higher than the inter-group edge density. A partition can be specified by labels assigned to the nodes in the network, and a group of nodes with the same label constitutes a community. Methods used to discover communities in static networks find a partition of nodes which optimizes some quality (objective) function that quantifies how community-like the partition is. For time-varying networks, given time snapshots, temporal community detection assigns labels to nodes in each snapshot, and the set of {node, time} pairs that get the same label constitutes a temporal community. We define a temporal community structure as a partitioning of the {node, time} pairs over all snapshots that optimizes an appropriate quality function. We focus on the sequential version of the temporal community detection problem, where one is allowed to do computations only on the current snapshot while using limited information from the past. Sequential methods are useful in situations where the number of snapshots is large, or fast computation of temporal communities is important as new snapshots become available. A popular approach to detecting temporal communities is to find static communities independently in each snapshot using some quality function and then ''map'' communities between snapshots to preserve labels when possible. Examples of this approach include the map-equation method 2 and the clique percolation method 3 . However, these methods do not explicitly use the partitions found in past snapshots to inform the search for the optimal partition on the current snapshot. We argue (and show empirically in Results) that mapping independently detected communities is likely to miss crucial temporal communities as most quality functions used for static community detection are highly degenerate and extremely sensitive to changes in the network. This has been demonstrated specifically for modularity 4 , one of the earliest proposed and still commonly used quality functions, though several others have subsequently been introduced. Good et al. 5 show that for many real-world networks, the modularity landscape is highly degenerate and disordered with numerous partitions yielding similar
Estrangement REF detects temporal communities by maximizing modularity in a snapshot subject to a constraint on the estrangement from the partition in the previous snapshot.
Sequential detection of temporal communities by estrangement confinement
Scientific Reports
Scientific Reports
Computer Science Medicine