The map equation

Abstract

Many real-world networks are so large that we must simplify their structure before we can extract useful information about the systems they represent. As the tools for doing these simplifications proliferate within the network literature, researchers would benefit from some guidelines about which of the so-called community detection algorithms are most appropriate for the structures they are studying and the questions they are asking. Here we show that different methods highlight different aspects of a network's structure and that the the sort of information that we seek to extract about the system must guide us in our decision. For example, many community detection algorithms, including the popular modularity maximization approach, infer module assignments from an underlying model of the network formation process. However, we are not always as interested in how a system's network structure was formed, as we are in how a network's extant structure influences the system's behavior. To see how structure influences current behavior, we will recognize that links in a network induce movement across the network and result in systemwide interdependence. In doing so, we explicitly acknowledge that most networks carry flow. To highlight and simplify the network structure with respect to this flow, we use the map equation. We present an intuitive derivation of this flow-based and information-theoretic method and provide an interactive on-line application that anyone can use to explore the mechanics of the map equation. The differences between the map equation and the modularity maximization approach are not merely conceptual. Because the map equation attends to patterns of flow on the network and the modularity maximization approach does not, the two methods can yield dramatically different results for some network structures. To illustrate this and build our understanding of each method, we partition several sample networks. We also describe an algorithm and provide source code to efficiently decompose large weighted and directed networks based on the map equation.

Default Mode Dynamics for Global Functional Integration

“…Thus, we initially used a whole-brain approach, in which average correlation matrices based on 264 ROIs (Power et al, 2011), corresponding to 10 well established LSNs, formed the basis of our functional connectivity and subsequent modularity analyses. The results, visualized via circular and novel alluvial representations (Rosvall et al, 2009), aimed to explicate the modular organization of the brain across task difficulty, but also were intended to clarify the change in communities formed by the LSNs and possible behavioral correlations. While the flexibility of the 264 nodes was assessed using the global variable connectivity measure, the DMN regions' nodal participation coefficient and strength were further scrutinized for a full characterization of DMNs' contribution to the global connectivity dynamics.…”

“…Having investigated the changes in modularity and the possible behavioral correlations across 22 subjects, our next objective was to clearly visualize the changes in community memberships responsible for the reconfiguration of the global brain modular architecture. The calculated communities were represented here using an alluvial diagram (Rosvall et al, 2009), which clearly outlines the interaction between LSNs at different difficulty levels, thus highlighting the flexible nodes that change community memberships. The 264 ROIs partitioning into 10 well established networks was color coded to aid the visualization of changes in community membership across the five distinct experimental conditions.…”

Translational Advances in the Field of Pulmonary Hypertension.Translating MicroRNA Biology in Pulmonary Hypertension. It Will Take More Than “miR” Words

“…(B) Network architecture analysis improves the resolution of testable hypotheses regarding convergent miRNA function. From genes targeted by four or more PH-relevant miRNAs and overlaid on an extended network of PH genes and their firstdegree interactors, a single connected component of 190 genes was partitioned into clusters based on its topology, using the "MAP" algorithm (58). Each node represents a gene, and each gray line denotes an interaction between genes.…”

Toward a route detection method base on detail call records

“…The idea behind this algorithm is to reduce the Map equation [6] by computing the fraction Require: k: of times a random walker visits a node. Based on those visits, a Greedy search algorithm is used to find a partition [16].…”