Higher-order motif analysis in hypergraphs

Abstract

A deluge of new data on real-world networks suggests that interactions among system units are not limited to pairs, but often involve a higher number of nodes. To properly encode higher-order interactions, richer mathematical frameworks such as hypergraphs are needed, where hyperedges describe interactions among an arbitrary number of nodes. Here we systematically investigate higher-order motifs, defined as small connected subgraphs in which vertices may be linked by interactions of any order, and propose an efficient algorithm to extract complete higher-order motif profiles from empirical data. We identify different families of hypergraphs, characterized by distinct higher-order connectivity patterns at the local scale. We also propose a set of measures to study the nested structure of hyperedges and provide evidences of structural reinforcement, a mechanism that associates higher strengths of higher-order interactions for the nodes that interact more at the pairwise level. Our work highlights the informative power of higher-order motifs, providing a principled way to extract higher-order fingerprints in hypergraphs at the network microscale.

Beyond the dyad: uncovering higher-order structure within cohesive animal groups

“…Secondly, higher-order networks provide greater social context to observed associations or interactions. For example, it might be of interest to distinguish if an individual participating in group interactions also forms connections with those individuals in smaller, pairwise, contexts, an insight which can be obtained through higher-order motif analysis (Lotito et al 2022). Similar reasoning applies to the mesoscale properties of a networked society.…”

“…For example, higher-order motif analysis (Lugo-Martinez et al . 2021; Lotito et al . 2022) revealed that clustered pairwise collaborations among scientific authors are predictive of future 3-way interactions (Benson et al .…”

“…Adopting a higher-order approach allows to effectively represent interactions and or associations that occur in groups of different sizes, helping in better understanding the structural differences between interacting agents that belong to different domains. For example, higher-order motif analysis (Lugo-Martinez et al 2021;Lotito et al 2022) revealed that clustered pairwise collaborations among scientific authors are predictive of future 3-way interactions (Benson et al 2018), and that protein or chemical compounds that interact in groups typically cannot do so in single pairs with other agents. In general, the decomposition of large hyperlinks (e.g.…”

Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

“…We observe weak evidence that more efficient markets have more stable structures. We study how simplicial motifs—patterns of edges which define simplicial complexes on a graph [ 26 , 27 ], e.g., edges, triangles and tetrahedra—are persisting or decaying through the time evolution of the filtered networks computed over a rolling time window. In order to test the multivariate long memory properties of financial time series, we compare the motif persistence in networks from real data with motif persistence from a range of null models [ 28 ]—corresponding to a range of parsimonious assumptions on the underlying generative processes—for groups of time series.…”

Understanding Hazardous Materials Transportation Accidents Based on Higher-Order Network Theory

“…Xu et al emphasized that it is important to consider the non-Markovian process when modeling sequential data and proposed a higher-order network representation and algorithm [ 18 , 34 ]. Lotito et al defined higher-order motifs as small connected subgraphs in which vertices may be linked by interactions of any order and proposed an efficient algorithm to extract complete higher-order motif profiles from empirical data [ 35 ]. Aktas et al proposed two new Laplacians that allowed redefining classical graph centrality measures for higher-order interactions [ 36 ].…”