Annotated hypergraphs: models and applications

Chodrow, Philip S.; Mellor, Andrew

doi:10.1007/s41109-020-0252-y

Cited by 43 publications

(34 citation statements)

References 62 publications

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“…The investigation of a mathematical structure that incorporates such information might be a fruitful extension to our work. Furthermore, one could consider the different role (e.g., catalyst) that proteins have in chemical reactions and investigate them as annotated hypergraphs [45].…”

Section: Discussionmentioning

confidence: 99%

Hypergraphs for predicting essential genes using multiprotein complex data

Klimm

Deane

Reinert

2020

Preprint

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Protein-protein interactions are crucial in many biological pathways and facilitate cellular function. Investigating these interactions as a graph of pairwise interactions can help to gain a systemic understanding of cellular processes. It is known, however, that proteins interact with each other not exclusively in pairs but also in polyadic interactions and they can form multiprotein complexes, which are stable interactions between multiple proteins. In this manuscript, we use hypergraphs to investigate multiprotein complex data. We investigate two random null models to test which hypergraph properties occur as a consequence of constraints, such as the size and the number of multiprotein complexes. We find that assortativity, the number of connected components, and clustering differ from the data to these null models. Our main finding is that projecting a hypergraph of polyadic interactions onto a graph of pairwise interactions leads to the identification of different proteins as hubs than the hypergraph. We find in our data set that the hypergraph degree is a more accurate predictor for gene-essentiality than the degree in the pairwise graph. We find that analysing a hypergraph as pairwise graph drastically changes the distribution of the local clustering coefficient. Furthermore, using a pairwise interaction representing multiprotein complex data may lead to a spurious hierarchical structure, which is not observed in the hypergraph. Hence, we illustrate that hypergraphs can be more suitable than pairwise graphs for the analysis of multiprotein complex data.

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Section: Discussionmentioning

confidence: 99%

Hypergraphs for predicting essential genes using multiprotein complex data

Klimm

Deane

Reinert

2020

Preprint

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“…We note that the above protocols of moving from one framework to another do not encompass all possibilities. One could define a simplicial complex from a graph by simply keeping all edges as the 1-skeleton and having no larger simplices, or perhaps one might form a weighted graph from a hypergraph by assigning edge weights as some function of the hypergraph structure [143,43,92]. Though we have here discussed moving between frameworks as the third step in the pipeline (see Figure 4.2), moving from one framework to another after the initial encoding of data into a formal representation should be performed only with extreme care, as any translation requires adding assumptions or the forgetting of relations or independencies.…”

Section: From Hypergraph To Simplicial Complex: Forgetting Independent Relationsmentioning

confidence: 99%

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

Torres¹,

Blevins²,

Bassett³

et al. 2021

SIAM Rev.

163

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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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“…Matamalas et al obtained a more accurate prediction of the spreading dynamics on simplicial complex [51]. Compared to simplicial complex, hypergraphs [52][53][54][55][56] do not require the appearance of all subsets in each interaction set, thus is more flexible in describing higher-order interactions. Hypergraph models, such as the uniform hypergraph, have been proposed to describe the higher-order interactions and to investigate the dynamics of group epidemic spreading [57,58].…”

Section: Introductionmentioning

confidence: 99%

Competing spreading dynamics in simplicial complex

Xue

Pan

et al. 2021

Preprint

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Interactions in biology and social systems are not restricted to pairwise but can take arbitrary sizes. Extensive studies have revealed that the arbitrary-sized interactions significantly affect the spreading dynamics on networked systems. Competing spreading dynamics, i.e., several epidemics spread simultaneously and compete with each other, have been widely observed in the real world, yet the way arbitrary-sized interactions affect competing spreading dynamics still lacks systematic study. This study presents a model of two competing simplicial susceptible-infected-susceptible epidemics on a higher-order system represented by simplicial complex and analyzes the model's critical phenomena. In the proposed model, a susceptible node can only be infected by one of the two epidemics, and the transmission of infection to neighbors can occur through pairwise (i.e., an edge) and high-order (e.g., 2-simplex) interactions simultaneously. Through a mean-field (MF) theory analysis and numerical simulations, we show that the model displays rich dynamical behavior depending on the 2-simplex infection strength. When the 2-simplex infection strength is weak, the model's phase diagram is consistent with the simple graph, consisting of three regions: the absolute dominant regions for each epidemic and the epidemic-free region. With the increase of the 2-simplex infection strength, a new phase region called the alternative dominant region emerges. In this region, the survival of one epidemic depends on the initial conditions. Our theoretical analysis can reasonably predict the time evolution and steady-state outbreak size in each region. In addition, we further explore the model's phase diagram both when the 2-simplex infection strength is symmetrical and asymmetrical. The results show that the 2-simplex infection strength has a significant impact on the system phase diagram.

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Annotated hypergraphs: models and applications

Cited by 43 publications

References 62 publications

Hypergraphs for predicting essential genes using multiprotein complex data

Hypergraphs for predicting essential genes using multiprotein complex data

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

Competing spreading dynamics in simplicial complex

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