Directed hypergraphs and applications

Gallo, Giorgio; Longo, G.; Pallottino, Stefano; Nguyen, Sang

doi:10.1016/0166-218x(93)90045-p

Cited by 544 publications

(458 citation statements)

References 16 publications

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“…A hypernetwork can be represented by a variety of different matrices (Gallo et al, 1993), the most popular of which is the incidence matrix, an n × m matrix C(H) representing the relationships between the n nodes and m hyperedges. The entries of the matrix C(H) are given by…”

Section: Hypernetwork Preliminariesmentioning

confidence: 99%

Complexity and robustness in hypernetwork models of metabolism

Pearcy

Chuzhanova

Crofts

2016

Journal of Theoretical Biology

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Metabolic reaction data is commonly modelled using a complex network approach, whereby nodes represent the chemical species present within the organism of interest, and connections are formed between those nodes participating in the same chemical reaction. Unfortunately, such an approach provides an inadequate description of the metabolic process in general, as a typical chemical reaction will involve more than two nodes, thus risking oversimplification of the the system of interest in a potentially significant way. In this paper, we employ a complex hypernetwork formalism to investigate the robustness of bacterial metabolic hypernetworks by extending the concept of a percolation process to hypernetworks. Importantly, this provides a novel method for determining the robustness of these systems and thus for quantifying their resilience to random attacks/errors. Moreover, we performed a site percolation analysis on a large cohort of bacterial metabolic networks and found that hypernetworks that evolved in more variable environments displayed increased levels of robustness and topological complexity.

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Section: Hypernetwork Preliminariesmentioning

confidence: 99%

Complexity and robustness in hypernetwork models of metabolism

Pearcy

Chuzhanova

Crofts

2016

Journal of Theoretical Biology

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“…Subfamilies of directed hypergraphs, as defined in Gallo et al (1993), can be associated with some earlier definitions, as the one presented in Ausiello et al (1985). Such subfamilies can be defined as follows:…”

Section: And Every Hyperedge Of H U Has a Corresponding Hyperarc In Hmentioning

confidence: 99%

“…A directed hypergraph (Gallo et al, 1993;Guedes, 2001) is defined as follows: In the undirected version of hypergraphs each hyperarc is considered as a set instead of a pair of sets, and is named hyperedge.…”

Section: Basic Notionsmentioning

confidence: 99%

“…Directed hypergraphs (Ausiello et al, 1985;Gallo et al, 1993) are a generalization of directed graphs (digraphs) and they can model binary relations among subsets of a given set. Such relationships appear in different areas of Computer Science such as database systems (Ausiello et al, 1985), expert systems (Ramaswamy et al, 1997), parallel programming (Nguyen et al, 1998), scheduling (Lin & Sarrafzadeh, 1995;Gallo & Scutellà, 2002), routing in dynamic networks (Pretolani, 2000) and, more recently, data mining (Chawla et al, 2004) and bioinformatics (Krishnamurthy et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

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Directed hypergraph planarity

Guedes

Markenzon

2005

Pesqui. Oper.

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Directed hypergraphs are generalizations of digraphs and can be used to model binary relations among subsets of a given set. Planarity of hypergraphs was studied by Johnson and Pollak; in this paper we extend the planarity concept to directed hypergraphs. It is known that the planarity of a digraph relies on the planarity of its underlying graph. However, for directed hypergraphs, this property do not apply and we propose a new approach which generalizes the usual concept. We also show that the complexity of the recognition of a directed hypergraph as planar is linear on the size of the hypergraph.Keywords: directed hypergraphs; planarity; algorithms. ResumoHipergrafos direcionados são generalizações de digrafos, e são utilizados na modelagem de relações binárias entre subconjuntos de um dado conjunto. O problema da planaridade em hipergrafos foi estudado por Johnson e Pollak; neste trabalho estendemos o conceito de planaridade para hipergrafos direcionados. É noção conhecida que a planaridade de hipergrafos depende da planaridade de seu grafo subjacente. Entretanto, para hipergrafos direcionados, esta propriedade não pode ser aplicada e propomos uma nova abordagem que generaliza o conceito tradicional. Mostramos também que a complexidade de testar a planaridade de um hipergrafo direcionado é linear no tamanho do hipergrafo.Palavras-chave: hipergrafos direcionados; planaridade; algoritmos.

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“…The value −1 stands for a sole source or access point of data available to the partner(s). A hyperlink with a −1 port and several positive fractional ports is a directed hyperarc of a specific kind called a backward hyperarc [7] (Fig. 5), and can be represented by a family of pointers pointing to the atom with the −1 port.…”

Section: Assigning Polarities and Capabilities To Links And Hyperlinksmentioning

confidence: 99%

Towards a Substrate Framework of Computation

Ueda

2014

Lecture Notes in Computer Science

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Abstract. A grand challenge in computing is to establish a substrate computational model that encompasses diverse forms of non-sequential computation. This paper demonstrates how a hypergraph rewriting framework nicely integrates various forms and ingredients of concurrent computation and how simple static analyses help the understanding and optimization of programs. Hypergraph rewriting treats processes and messages in a unified manner, and treats message sending and parameter passing as symmetric reaction between two entities. Specifically, we show how fine-grained strong reduction of the λ-calculus can be concisely encoded into hypergraph rewriting with a small set of primitive operations.

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Directed hypergraphs and applications

Cited by 544 publications

References 16 publications

Complexity and robustness in hypernetwork models of metabolism

Complexity and robustness in hypernetwork models of metabolism

Directed hypergraph planarity

Towards a Substrate Framework of Computation

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