MapEquation

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Code »

using infomath::plogp;
for (unsigned int i = 0; i < numNodes; ++i)
{
enter_log_enter += plogp(m_moduleFlowData[i].enterFlow);
exit_log_exit += plogp(m_moduleFlowData[i].exitFlow);
flow_log_flow += plogp(m_moduleFlowData[i].exitFlow + m_moduleFlowData[i].flow);
enterFlow += m_moduleFlowData[i].enterFlow;
}
enterFlow += exitNetworkFlow;
enterFlow_log_enterFlow = plogp(enterFlow);

indexCodelength = enterFlow_log_enterFlow - enter_log_enter - exitNetworkFlow_log_exitNetworkFlow;
moduleCodelength = -exit_log_exit + flow_log_flow - nodeFlow_log_nodeFlow;
codelength = indexCodelength + moduleCodelength;

Publications »

Maps of information flow reveal community structure in complex networks Martin Rosvall and Carl T. Bergstrom PNAS 105, 1118 (2008). [arXiv:0707.0609]

To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information-theoretic approach to reveal community structure in weighted and directed networks. The method decomposes a network into modules by optimally compressing a description of information flows on the network. The result is a map that both simplifies and highlights the regularities in the structure and their relationships to each other. We illustrate the method by making a map of scientific communication as captured in the citation patterns of more than 6000 journals. We discover a multicentric organization with fields that vary dramatically in size and degree of integration into the network of science. Along the backbone of the network — which includes physics, chemistry, molecular biology, and medicine — information flows bidirectionally, but the map reveals a directional pattern of citation from the applied fields to the basic sciences.