dorsal/arxiv
View SchemaComplex Networks as Hypergraphs
| Authors | Ernesto Estrada, Juan A. Rodriguez-Velazquez |
|---|---|
| Categories | |
| ArXiv ID | physics/0505137 |
| URL | https://arxiv.org/abs/physics/0505137 |
| DOI | 10.1016/j.physa.2005.12.002 |
Abstract
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited information about the structure of the system. We propose to use hypergraphs to represent these systems by introducing the concept of the complex hyper-network. We define several structural measures for complex hyper-networks. These measures characterize hyper-network structures on the basis of node participation in different hyper-edges (groups) and sub-hypergraphs. We also define two clustering coefficients, one characterizing the transitivity in the hyper-network through the proportion of hyper-triangles to paths of length two and the other characterizing the formation of triples of mutually adjacent groups in the hyper-network. All of these characteristics are studied in two different hyper-networks; a scientific collaboration hyper-network and an ecological competence hyper-network.
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"abstract": "The representation of complex systems as networks is inappropriate for the\nstudy of certain problems. We show several examples of social, biological,\necological and technological systems where the use of complex networks gives\nvery limited information about the structure of the system. We propose to use\nhypergraphs to represent these systems by introducing the concept of the\ncomplex hyper-network. We define several structural measures for complex\nhyper-networks. These measures characterize hyper-network structures on the\nbasis of node participation in different hyper-edges (groups) and\nsub-hypergraphs. We also define two clustering coefficients, one characterizing\nthe transitivity in the hyper-network through the proportion of hyper-triangles\nto paths of length two and the other characterizing the formation of triples of\nmutually adjacent groups in the hyper-network. All of these characteristics are\nstudied in two different hyper-networks; a scientific collaboration\nhyper-network and an ecological competence hyper-network.",
"arxiv_id": "physics/0505137",
"authors": [
"Ernesto Estrada",
"Juan A. Rodriguez-Velazquez"
],
"categories": [
"physics.soc-ph"
],
"doi": "10.1016/j.physa.2005.12.002",
"title": "Complex Networks as Hypergraphs",
"url": "https://arxiv.org/abs/physics/0505137"
},
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