Analyzing, Exploring, and Visualizing Complex Networks via Hypergraphs using SimpleHypergraphs.jl

Abstract

Real-world complex networks are usually being modeled as graphs. The concept of graphs assumes that the relations within the network are binary (for instance, between pairs of nodes); however, this is not always true for many real-life scenarios, such as peer-to-peer communication schemes, paper co-authorship, or social network interactions. For such scenarios, it is often the case that the underlying network is better and more naturally modeled by hypergraphs. A hypergraph is a generalization of a graph in which a single (hyper)edge can connect any number of vertices. Hypergraphs allow modelers to have a complete representation of multi-relational (many-to-many) networks; hence, they are extremely suitable for analyzing and discovering more subtle dependencies in such data structures. Working with hypergraphs requires new software libraries that make it possible to perform operations on them, from basic algorithms (such as searching or traversing the network) to computing significant hypergraph measures, to including more challenging algorithms (such as community detection). In this paper, we present a new software library, SimpleHypergraphs.jl, written in the Julia language and designed for high-performance computing on hypergraphs and propose two new algorithms for analyzing their properties: s-betweenness and modified label propagation. We also present various approaches for hypergraph visualization integrated into our tool. In order to demonstrate how to exploit the library in practice, we discuss two case studies based on the 2019 Yelp Challenge dataset and the collaboration network built upon the Game of Thrones TV series. The results are promising and they confirm the ability of hypergraphs to provide more insight than standard graph-based approaches.

Social Influence Maximization in Hypergraphs

“…In other words, a hyperedge consists of all characters appearing in the same scene together. More details about this data set are given in [ 37 ].…”

Not your private tête-à-tête: leveraging the power of higher-order networks to study animal communication

“…Basic tools for working with hypergraphs and simplicial complexes are also available in Julia (e.g. SimpleHypergraphs.jl: [77] and Simplicial.jl: https://github.com/nebneuron/Simplicial.jl).…”

What Are Higher-Order Networks?

“…The cost of such methods, however, is that higher-order relationships and structure are lost, as well as some meaning. For example, analyzing collaboration networks as graphs versus hypergraphs has been compared and contrasted in several papers with each of these articles illustrating new insights that can be gained when thinking about a collaboration network as a hypergraph [105,170,199,274]. Having tools for higher-order networks, such as those discussed in this review, allow such analysis to be possible, and, importantly, invites us to be more conscious about the choices that we are making when analyzing data.…”