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

Complex numbers define the relationship between entities in many situations.A canonical example would be the off-diagonal terms in a Hamiltonian matrix inquantum physics. Recent years have seen an increasing interest to extend thetools of network science when the weight of edges are complex numbers. Here, wefocus on the case when the weight matrix is Hermitian, a reasonable assumptionin many applications, and investigate both structural and dynamical propertiesof the complex-weighted networks. Building on concepts from signed graphs, weintroduce a classification of complex-weighted networks based on the notion ofstructural balance, and illustrate the shared spectral properties within eachtype. We then apply the results to characterise the dynamics of random walks oncomplex-weighted networks, where local consensus can be achieved asymptoticallywhen the graph is structurally balanced, while global consensus will beobtained when it is strictly unbalanced. Finally, we explore potentialapplications of our findings by generalising the notion of cut, and propose anassociated spectral clustering algorithm. We also provide furthercharacteristics of the magnetic Laplacian, associating directed networks tocomplex-weighted ones. The performance of the algorithm is verified on bothsynthetic and real networks.

Structural Balance and Random Walks on Complex Networks with Complex Weights