On using undirected graph techniques for directed graphs through Category Theory Article Swipe
Sebastian Prado Guerra
,
Vivek Kurien George
,
Vikash Morar
,
Roldan Joshua
,
Gabriel da Silva
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.21203/rs.3.rs-1995489/v1
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.21203/rs.3.rs-1995489/v1
Many complex systems are modeled as graphs. Depending on the setting, graphs can be either directed or undirected. While many computational tools have been developed for both types of graphs, some tools only exist for undirected graphs. Thus, creating a ’bridge’ that connects directed graphs to undirected graphs would unlock the potential for using undirected graph techniques in appropriate directed graph contexts. We used Category Theory in a novel way to map a simple directed graph to a bipartite undirected graph that we call a prime graph. Formally, we show that there exists an isomorphism between the category of simple directed graphs and a category of prime graphs whose objects are labeled undirected bipartite graphs. The labeling is what gives the notion of direction to an undirected graph. By taking advantage of the isomorphism between these two categories, we extend undirected graph techniques to directed graph contexts by converting the directed graphs into prime graphs. We demonstrate this framework by applying it to the problems of network alignment and spectral graph clustering.
Related Topics
Concepts
Comparability graph
Modular decomposition
Combinatorics
Undirected graph
Graph isomorphism
Line graph
Cograph
Block graph
Indifference graph
Mathematics
Chordal graph
Pathwidth
Directed graph
Bipartite graph
Discrete mathematics
Graph product
Computer science
Graph
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.21203/rs.3.rs-1995489/v1
- OA Status
- gold
- References
- 17
- Related Works
- 10
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W4293463670Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.21203/rs.3.rs-1995489/v1Digital Object Identifier
- Title
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On using undirected graph techniques for directed graphs through Category TheoryWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-08-29Full publication date if available
- Authors
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Sebastian Prado Guerra, Vivek Kurien George, Vikash Morar, Roldan Joshua, Gabriel da SilvaList of authors in order
- Landing page
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https://doi.org/10.21203/rs.3.rs-1995489/v1Publisher landing page
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.21203/rs.3.rs-1995489/v1Direct OA link when available
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Comparability graph, Modular decomposition, Combinatorics, Undirected graph, Graph isomorphism, Line graph, Cograph, Block graph, Indifference graph, Mathematics, Chordal graph, Pathwidth, Directed graph, Bipartite graph, Discrete mathematics, Graph product, Computer science, GraphTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.While | 19 |
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| abstract_inverted_index.gives | 120 |
| abstract_inverted_index.graph | 56, 61, 76, 81, 142, 146, 171 |
| abstract_inverted_index.novel | 69 |
| abstract_inverted_index.prime | 86, 107, 154 |
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| abstract_inverted_index.tools | 22, 32 |
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| abstract_inverted_index.Theory | 66 |
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| abstract_inverted_index.extend | 140 |
| abstract_inverted_index.graph. | 87, 128 |
| abstract_inverted_index.graphs | 12, 45, 48, 102, 108, 152 |
| abstract_inverted_index.notion | 122 |
| abstract_inverted_index.simple | 74, 100 |
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| abstract_inverted_index.unlock | 50 |
| abstract_inverted_index.between | 96, 135 |
| abstract_inverted_index.complex | 2 |
| abstract_inverted_index.graphs, | 30 |
| abstract_inverted_index.graphs. | 7, 37, 115, 155 |
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| abstract_inverted_index.modeled | 5 |
| abstract_inverted_index.network | 167 |
| abstract_inverted_index.objects | 110 |
| abstract_inverted_index.systems | 3 |
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| abstract_inverted_index.computational | 21 |
| abstract_inverted_index.<title>Abstract</title> | 0 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5004403965 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 5 |
| corresponding_institution_ids | https://openalex.org/I36258959 |
| citation_normalized_percentile.value | 0.12587477 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |