Clustering via hypergraph modularity

Kamiński, Bogumił; Poulin, Valérie; Prałat, Paweł; Szufel, Przemysław; Théberge, François

doi:10.1371/journal.pone.0224307

Cited by 58 publications

(69 citation statements)

References 31 publications

(34 reference statements)

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“…While these models were inspired from their graph counterparts and named as such, there may be multiple ways of conceiving these models in the hypergraph/bicolored graph setting, as is often the case with graph-to-hypergraph extensions. In fact, others have proposed non-uniform hypergraph analogs of Erdős-Rényi and Chung-Lu (see [8] and [71], respectively) differing to those considered here with regard to the inputs required, the model itself, and the definition of hypergraph assumed.…”

Section: Comparison With Generative Hypergraph Null Modelsmentioning

confidence: 97%

“…In comparison to their graph counterparts, generative hypergraph models are relatively few. While work on random uniform hypergraphs dates back to at least the 1970s, researchers have recently begun developing a wider variety of hypergraph models, both for uniform hypergraphs [38][39][40]67] and non-uniform hypergraphs [8,[68][69][70][71]. We consider three generative hypergraph models from [65], which can be thought of as hypergraph interpretations of the graph models Erdős-Rényi (ER) [72], Chung-Lu (CL) [73], and Block Two-Level Erdős-Rényi (BTER) [74,75].…”

Section: Comparison With Generative Hypergraph Null Modelsmentioning

confidence: 99%

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Hypernetwork science via high-order hypergraph walks

et al. 2020

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We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.

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Section: Comparison With Generative Hypergraph Null Modelsmentioning

confidence: 97%

Section: Comparison With Generative Hypergraph Null Modelsmentioning

confidence: 99%

Hypernetwork science via high-order hypergraph walks

et al. 2020

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“…Many such extensions are possible. Unlike a recent proposal [23], we define a dyadic notion of modularity via null expectations for the weighted projected graph computed via Equation (7). While our approach loses some higher-order information in the modularity calculation, it has the benefit of allowing roles to be flexibly incorporated into the null expectation.…”

Section: Modularity and Community Detectionmentioning

confidence: 99%

Annotated hypergraphs: models and applications

Chodrow

Mellor

2020

Appl Netw Sci

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Hypergraphs offer a natural modeling language for studying polyadic interactions between sets of entities. Many polyadic interactions are asymmetric, with nodes playing distinctive roles. In an academic collaboration network, for example, the order of authors on a paper often reflects the nature of their contributions to the completed work. To model these networks, we introduce annotated hypergraphs as natural polyadic generalizations of directed graphs. Annotated hypergraphs form a highly general framework for incorporating metadata into polyadic graph models. To facilitate data analysis with annotated hypergraphs, we construct a role-aware configuration null model for these structures and prove an efficient Markov Chain Monte Carlo scheme for sampling from it. We proceed to formulate several metrics and algorithms for the analysis of annotated hypergraphs. Several of these, such as assortativity and modularity, naturally generalize dyadic counterparts. Other metrics, such as local role densities, are unique to the setting of annotated hypergraphs. We illustrate our techniques on six digital social networks, and present a detailed case-study of the Enron email data set.

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“…Table 3 contains the modularity values for the 6 different partitions evaluated. To calculate the modularity, we used the approach presented in [44] and implemented in SimpleHypergraphs.jl (see Section 3.4).…”

Section: Exploring and Analyzing User Reviews: Yelpcommentioning

confidence: 99%

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

Spagnuolo¹,

Cordasco²,

Szufel³

et al. 2020

Internet Mathematics

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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.

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Clustering via hypergraph modularity

Cited by 58 publications

References 31 publications

Hypernetwork science via high-order hypergraph walks

Hypernetwork science via high-order hypergraph walks

Annotated hypergraphs: models and applications

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

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