Constrained information flows in temporal networks reveal intermittent communities

Abstract

Many real-world networks represent dynamic systems with interactions that change over time, often in uncoordinated ways and at irregular intervals. For example, university students connect in intermittent groups that repeatedly form and dissolve based on multiple factors, including their lectures, interests, and friends. Such dynamic systems can be represented as multilayer networks where each layer represents a snapshot of the temporal network. In this representation, it is crucial that the links between layers accurately capture real dependencies between those layers. Often, however, these dependencies are unknown. Therefore, current methods connect layers based on simplistic assumptions that do not capture node-level layer dependencies. For example, connecting every node to itself in other layers with the same weight can wipe out dependencies between intermittent groups, making it difficult or even impossible to identify them. In this paper, we present a principled approach to estimating node-level layer dependencies based on the network structure within each layer. We implement our node-level coupling method in the community detection framework Infomap and demonstrate its performance compared to current methods on synthetic and real temporal networks. We show that our approach more effectively constrains information inside multilayer communities so that Infomap can better recover planted groups in multilayer benchmark networks that represent multiple modes with different groups and better identify intermittent communities in real temporal contact networks. These results suggest that node-level layer coupling can improve the modeling of information spreading in temporal networks and better capture intermittent community structure.

Seeing the forest for the trees: Putting multilayer networks to work for community ecology

“…It is also possible to infer inter‐layer edges based on intra‐layer edges. Neighborhood flow coupling—where inter‐layer weights are designated based on the similarity of a node's intra‐layer edges between two layers—provides one approach to do so (Aslak, Rosvall, & Lehmann, ) and would be appropriate for temporal and spatial EMNs. For example, if a plant is visited by the same pollinators in two consecutive years, this approach would generate a strong inter‐layer link between the plant species in those two layers likely implying maintenance of abundance and pollination service between years.…”

A multiscale view of the Phanerozoic fossil record reveals the three major biotic transitions

“…The map equation multilayer framework consists of an objective function that measures the quality of a given network partition, the map equation itself (23), and Infomap, an efficient search algorithm that optimizes this function over different solutions (21). We used this method because it can handle bipartite, weighted, and multilayer networks and because it is known for its high performance (36)(37)(38). In addition, 185…”

“…Infomap directly provides the number of hierarchical levels within each layer and thus removes the subjectivity inherent in other approaches (38).…”

“…Infomap can identify these modules because using modules in which the random walker persists for relatively long periods optimizes the map equation, which measures how much a modular partition of the nodes can compress a description of the random walker on the network. Following previous network studies, we used the relax rate = 0.25, which is large enough to 200 enable interlayer interdependencies but small enough to preserve intralayer information (38). We tested the robustness to the selected relax rate by clustering the assembled network for a range of relax rates and comparing each solution to the solution for = 0.25 using the Jaccard Similarity.…”

“…Results are particularly robust in the domain r ≥ 0.20. Following previous studies on complex networks, we used a relax rate r = 0.25 for the reference solution, which is large enough to enable interlayer interdependencies but small enough to preserve intralayer information (38). Figure S6.…”