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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Much effort has gone into understanding the modular nature of complexnetworks. Communities, also known as clusters or modules, are typicallyconsidered to be densely interconnected groups of nodes that are only sparselyconnected to other groups in the network. Discovering high quality communitiesis a difficult and important problem in a number of areas. The most popularapproach is the objective function known as modularity, used both to discovercommunities and to measure their strength. To understand the modular structureof networks it is then crucial to know how such functions evaluate differenttopologies, what features they account for, and what implicit assumptions theymay make. We show that trees and treelike networks can have unexpectedly andoften arbitrarily high values of modularity. This is surprising since trees aremaximally sparse connected graphs and are not typically considered to possessmodular structure, yet the nonlocal null model used by modularity assigns lowprobabilities, and thus high significance, to the densities of these sparsetree communities. We further study the practical performance of popular methodson model trees and on a genealogical data set and find that the discoveredcommunities also have very high modularity, often approaching its maximumvalue. Statistical tests reveal the communities in trees to be significant, incontrast with known results for partitions of sparse, random graphs.

Communities and bottlenecks: Trees and treelike networks have high modularity