A Topological Approach to Representational Data Models

Purvine, Emilie; Aksoy, Sinan; Joslyn, Cliff; Nowak, Kathleen; Praggastis, Brenda; Robinson, Michael

doi:10.1007/978-3-319-92043-6_8

Cited by 12 publications

(8 citation statements)

References 45 publications

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“…Indeed, one of the earliest practical uses of hypergraphs was to understand social networks [186]. Since then, researchers have successfully employed hypergraphs to study polyadic relations in the Enron email dataset [164], find the core of yeast proteinprotein interactions [165], uncover motifs in neurodevelopment [90], track changes in evolving systems [19,57,58], and detect failure in biochemical networks [111]. As many uses of hypergraphs arose out of systems first modeled with graphs, many analysis methods for hypergraphs mimic those originally used for graphs (we discuss this point further in section 5.3).…”

Section: Hypergraphsmentioning

confidence: 99%

The Why, How, and When of Representations for Complex Systems

Torres¹,

Blevins²,

Bassett³

et al. 2021

SIAM Rev.

179

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Complex systems, composed at the most basic level of units and their interactions, describe phenomena in a wide variety of domains, from neuroscience to computer science and economics. The wide variety of applications has resulted in two key challenges: the generation of many domain-specific strategies for complex systems analyses that are seldom revisited, and the compartmentalization of representation and analysis ideas within a domain due to inconsistency in complex systems language. In this work we propose basic, domain-agnostic language in order to advance toward a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system under study and data collected, then moving through different mathematical frameworks for encoding the observed data (i.e., graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each framework. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of an interaction among a set of units in a system may affect the possibility of the existence of another relation. We discuss how dependencies may arise and how they may alter the interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and the choice of mathematical representation influence the results. We hope this work can serve as an opportunity for reflection for experienced complex systems scientists, as well as an introductory resource for new researchers.

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Section: Hypergraphsmentioning

confidence: 99%

The Why, How, and When of Representations for Complex Systems

Torres¹,

Blevins²,

Bassett³

et al. 2021

SIAM Rev.

179

View full text Add to dashboard Cite

show abstract

“…They conduct a rigorous mathematical analysis of the asymptotic s-walk properties of binomial random k-uniform hypergraphs, considering hitting times, the evolution of high-order s-components, and high-order "hypertree" structures. Lastly, in [41,42], authors of the present work briefly considered the s-walk based notion of s-distance as applied to Domain Name System (DNS) cyber data, and the Enron email dataset, respectively.…”

Section: From Graph Walks To Hypergraph Walksmentioning

confidence: 99%

Hypernetwork science via high-order hypergraph walks

et al. 2020

Self Cite

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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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“…Indeed one of the earliest practical uses of hypergraphs was to understand social networks [177]. Since then, researchers have successfully employed hypergraphs to study polyadic relations in the Enron email dataset [156], find the core of yeast protein-protein interactions [157], uncover motifs in neurodevelopment [84], track changes in evolving systems [17,52,53], and detect failure in biochemical networks [105]. As many uses of hypergraphs arose out of systems first modeled with graphs, many analysis methods for hypergraphs mimic those originally used for graphs (we discuss this point further in Section 5.3).…”

Section: Hypergraphsmentioning

confidence: 99%

The why, how, and when of representations for complex systems

Torres¹,

Blevins²,

Bassett³

et al. 2020

Preprint

View full text Add to dashboard Cite

Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific strategies that are seldom revisited or questioned, and the siloing of ideas within a domain due to inconsistency of complex systems language. In this work we offer basic, domain-agnostic language in order to advance towards a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system and data collected, then moving through different mathematical formalisms for encoding the observed data (i.e. graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each formalism. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of one relation among the parts of a system may influence the existence of another relation. We discuss how dependencies may arise and how they may alter interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and choice of mathematical representation influence the results. We hope this work can serve as an opportunity of reflection for experienced complexity scientists, as well as an introductory resource for new researchers.

show abstract

A Topological Approach to Representational Data Models

Cited by 12 publications

References 45 publications

The Why, How, and When of Representations for Complex Systems

The Why, How, and When of Representations for Complex Systems

Hypernetwork science via high-order hypergraph walks

The why, how, and when of representations for complex systems

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