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To better understand the overlapping modular organization of large networks with respect to flow, here 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… (More)

Capturing dynamics of the spread of information and disease with random flow on networks is a paradigm. We show that this conventional approach ignores an important feature of the dynamics: where flow moves to depends on where it comes from. That is, memory matters. We analyze multi-step pathways from different systems and show that ignoring memory… (More)

To better understand the inner workings of information spreading, network researchers often use simple models to capture the spreading dynamics. But most models only highlight the effect of local interactions on the global spreading of a single information wave, and ignore the effects of interactions between multiple waves. Here we take into account the… (More)

As the number of scientific journals has multiplied, journal rankings have become increasingly important for scientific decisions. From submissions and subscriptions to grants and hirings, researchers, policy makers, and funding agencies make important decisions with influence from journal rankings such as the ISI journal impact factor. Typically, the… (More)

In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a node can belong to more than one module. In our proposed solution, the underlying stochastic process used to compare… (More)

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