Hypergraph Motifs:
Concepts, Algorithms, and Discoveries


We propose Hypergraph Motifs (h-motifs), whose occurrences capture local structural patterns of real-world hypergraphs.
H-motifs describe connectivity patterns of three connected hyperedges with the following properties:
MoCHy (Motif Counting in Hypergraphs) is a family of parallel algorithms for counting h-motifs' occurrences in a hypergraph.



The source code used in the paper is available. [Code]


We use the following 11 real-world hypergraphs from 5 different domains after removing duplicated hyperedges:

Dataset# Nodes# Hyperedges# Hyperwedges# H-motifsDomainSource
coauth-DBLP1.9M2.4M125M26.3B Co-authorship Link
coauth-geology1.2M1.2M37.6M6B Co-authorship Link
coauth-history1.0M895K1.7M83.2M Co-authorship Link
contact-primary24212.7K2.2M617M Contact Link
contact-high3277.8K593K69.7M Contact Link
email-Enron1431.5K87.8K9.6M E-mail Link
email-EU99825K8.3M7B E-mail Link
tags-ask-ubuntu3.0K147K564M4.3T Tags Link
tags-math-sx1.6K170K913M9.2T Tags Link
threads-ask-ubuntu125K166K21.6M11.4B Threads Link
threads-math-sx176K595K647M2.2T Threads Link