Compression of Flow Can Reveal Overlapping-Module Organization in Networks

Abstract

To better understand the organization of overlapping modules in large networks with respect to flow, we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between compression and regularity detection. The generalized map equation measures how well we can compress a description of flow in the network when we partition it into modules with possible overlaps. When we minimize the generalized map equation over overlapping network partitions, we detect modules that capture flow and determine which nodes at the boundaries between modules should be classified in multiple modules and to what degree. With a novel greedy-search algorithm, we find that some networks, for example, the neural network of the nematode Caenorhabditis elegans, are best described by modules dominated by hard boundaries, but that others, for example, the sparse European-roads network, have an organization of highly overlapping modules.

Mapping the global network of fisheries science collaboration

“…Detecting communities in networks (e.g., social, biological, citation, metabolic networks) can generally be classified into discovering non‐overlapping communities where each node belongs to a single community (Blondel et al, ; Clauset, Newman, & Moore, ; Decelle, Krzakala, Moore, & Zdeborová, , ; Fortunato, ; Hofman & Wiggins, ; Newman & Girvan, ; Newman & Leicht, ; Nowicki & Snijders, ), or overlapping communities where nodes can belong to several communities (Ahn, Bagrow, & Lehmann, ; Airoldi, Blei, Fienberg, & Xing, ; Ball, Karrer, & Newman, ; Derényi, Palla, & Vicsek, ; Gopalan & Blei, ; Gregory, ; Lancichinetti, Radicchi, Ramasco, & Fortunato, ; Viamontes Esquivel & Rosvall, ). Increasingly, real‐world networks can be characterised as overlapping (Palla et al, ), and the most general formulation of a community detection algorithm should ideally include both overlapping and non‐overlapping communities (Ball et al, ).…”

“…We performed a grid search ( Figure S1) on the hyper-parameter (i.e., resolution) space and, due to the heuristic nature of the Louvain algorithm, conducted 10 different random initialisations for each grid search. In doing so, we aimed to find the hyper-parameters that resulted in communities with high modularity (Newman, 2003;Newman & Girvan, 2004) Detecting communities in networks (e.g., social, biological, citation, metabolic networks) can generally be classified into discovering non-overlapping communities where each node belongs to a single community (Blondel et al, 2008;Clauset, Newman, & Moore, 2004;Decelle, Krzakala, Moore, & Zdeborová, 2011a, 2011bFortunato, 2010;Hofman & Wiggins, 2008;Newman & Girvan, 2004;Newman & Leicht, 2007;Nowicki & Snijders, 2001), or overlapping communities where nodes can belong to several communities (Ahn, Bagrow, & Lehmann, 2010;Airoldi, Blei, Fienberg, & Xing, 2008;Ball, Karrer, & Newman, 2011;Gopalan & Blei, 2013;Gregory, 2010;Lancichinetti, Radicchi, Ramasco, & Fortunato, 2011;Viamontes Esquivel & Rosvall, 2011). Increasingly, real-world networks can be characterised as overlapping , and the most general formulation of a community detection algorithm should ideally include both overlapping and non-overlapping communities (Ball et al, 2011).…”

Community detection in networks: A user guide

“…In the latter case, random walk dynamics is modified by introducing a teleportation probability, as in the PageRank process (Brin and Page, 1998), to ensure that a nontrivial stationary state is reached. It has been successively extended to the detection of hierarchical community structure (Rosvall and Bergstrom, 2011) and of overlapping clusters (Viamontes Esquivel and Rosvall, 2011). In classic random walks the probability of reaching a vertex only depends on where the walker stands, not on where it is coming from.…”

“…It has a dedicated website http://www.mapequation.org, where several extensions can be downloaded, including hierarchical community structure (Rosvall and Bergstrom, 2011), overlapping clusters (Viamontes Esquivel and Rosvall, 2011) and memory (Rosvall et al, 2014). Infomap has also its own functions on igraph, both in the R and in the Python package (cluster infomap and community infomap, respectively).…”

How to Draw a Neighborhood? The Potential of Big Data, Regionalization, and Community Detection for Understanding the Heterogeneous Nature of Urban Neighborhoods

“…), or based on the tweet content (e.g., supporting different political candidates, tweeting about specific social or cultural behavior), and so on. We have also not fully explored the affordances of the Infomap approach to community detection in this regard, as it also allows for explicit fuzzy boundaries and overlap (Viamontes Esquivel and Rosvall ), hierarchical clustering (Rosvall and Bergstrom ), and multilayered communities that include different types of ties (e.g., positive and negative connections) (De Domenico et al ).…”