English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

To comprehend the hierarchical organization of large integrated systems, weintroduce the hierarchical map equation, which reveals multilevel structures innetworks. In this information-theoretic approach, we exploit the dualitybetween compression and pattern detection; by compressing a description of arandom walker as a proxy for real flow on a network, we find regularities inthe network that induce this system-wide flow. Finding the shortest multileveldescription of the random walker therefore gives us the best hierarchicalclustering of the network, the optimal number of levels and modular partitionat each level, with respect to the dynamics on the network. With a novel searchalgorithm, we extract and illustrate the rich multilevel organization ofseveral large social and biological networks. For example, from the global airtraffic network we uncover countries and continents, and from the pattern ofscientific communication we reveal more than 100 scientific fields organized infour major disciplines: life sciences, physical sciences, ecology and earthsciences, and social sciences. In general, we find shallow hierarchicalstructures in globally interconnected systems, such as neural networks, andrich multilevel organizations in systems with highly separated regions, such asroad networks.

Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems