Graphlets in multilayer networks

Sallamari Sallmen, Tarmo Nurmi*, Mikko Kivelä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
53 Downloads (Pure)


Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these systems. We introduce a general and principled graphlet framework for multilayer networks which allows one to break any multilayer network into small multilayered building blocks. These multilayer graphlets can be either analysed themselves or used to do tasks such as comparing different systems. The method is flexible in terms of multilayer isomorphism, automorphism orbit definition and the type of multilayer network. We illustrate our method for multiplex networks and show how it can be used to distinguish networks produced with multiple models from each other in an unsupervised way. In addition, we include an automatic way of generating the hundreds of dependency equations between the orbit counts needed to remove redundant orbit counts. The framework introduced here allows one to analyse multilayer networks with versatile semantics, and these methods can thus be used to analyse the structural building blocks of myriad multilayer networks.

Original languageEnglish
Article numbercnac005
JournalJournal of Complex Networks
Issue number2
Publication statusPublished - 6 Apr 2022
MoE publication typeA1 Journal article-refereed


  • graph distance
  • graphlets
  • Multilayer networks
  • multiplex networks


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