Hybrid graph theory and network analysis:
First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the do...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Schriftenreihe: | Cambridge tracts in theoretical computer science
49 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1017/CBO9780511666391 https://doi.org/10.1017/CBO9780511666391 https://doi.org/10.1017/CBO9780511666391 |
| Zusammenfassung: | First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Umfang: | 1 online resource (x, 176 pages) |
| ISBN: | 9780511666391 |
| DOI: | 10.1017/CBO9780511666391 |
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| 505 | 8 | |a 1. Two Dual Structures of a Graph. 1.1. Basic concepts of graphs. 1.2. Cuts and circs. 1.3. Cut and circ spaces. 1.4. Relationships between cut and circ spaces. 1.5. Edge-separators and connectivity | |
| 505 | 8 | |a 1.6. Equivalence relations among graphs. 1.7. Directed graphs. 1.8. Networks and multiports. 1.9. Kirchhoff's laws. 1.10. Bibliographic notes -- 2. Independence Structures. 2.1. The graphoidal point of view | |
| 505 | 8 | |a 2.2. Independent collections of circs and cuts. 2.3. Maximal circless and cutless sets. 2.4. Circ and cut vector spaces. 2.5. Binary graphoids and their representations. 2.6. Orientable binary graphoids and Kirchhoff's laws | |
| 505 | 8 | |a 2.7. Mesh and nodal analysis. 2.8. Bibliographic notes -- 3. Basoids. 3.1. Preliminaries. 3.2. Basoids of graphs. 3.3. Transitions from one basoid to another. 3.4. Minor with respect to a basoid. 3.5. Principal sequence | |
| 505 | 8 | |a 3.6. Principal minor and principal partition. 3.7. Hybrid rank and basic pairs of subsets. 3.8. Hybrid analysis of networks. 3.9. Procedure for finding an optimal basic pair. 3.10. Bibliographic notes -- 4. Pairs of Trees | |
| 505 | 8 | |a 4.1. Diameter of a tree. 4.2. Perfect pairs of trees. 4.3. Basoids and perfect pairs of trees. 4.4. Superperfect pairs of trees. 4.5. Unique solvability of affine networks. 4.6. Bibliographic notes | |
| 505 | 8 | |a 5. Maximally Distant Pairs of Trees. 5.1. Preliminaries. 5.2. Minor with respect to a pair of trees. 5.3. Principal sequence. 5.4. The principal minor. 5.5. Hybrid pre-rank and the principal minor | |
| 505 | 8 | |a 5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes | |
| 520 | |a First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved | ||
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Datensatz im Suchindex
| _version_ | 1818982569337683968 |
|---|---|
| any_adam_object | |
| author | Novak, Ladislav 1950- |
| author_facet | Novak, Ladislav 1950- |
| author_role | aut |
| author_sort | Novak, Ladislav 1950- |
| author_variant | l n ln |
| building | Verbundindex |
| bvnumber | BV043942157 |
| classification_rvk | SK 890 |
| collection | ZDB-20-CBO |
| contents | 1. Two Dual Structures of a Graph. 1.1. Basic concepts of graphs. 1.2. Cuts and circs. 1.3. Cut and circ spaces. 1.4. Relationships between cut and circ spaces. 1.5. Edge-separators and connectivity 1.6. Equivalence relations among graphs. 1.7. Directed graphs. 1.8. Networks and multiports. 1.9. Kirchhoff's laws. 1.10. Bibliographic notes -- 2. Independence Structures. 2.1. The graphoidal point of view 2.2. Independent collections of circs and cuts. 2.3. Maximal circless and cutless sets. 2.4. Circ and cut vector spaces. 2.5. Binary graphoids and their representations. 2.6. Orientable binary graphoids and Kirchhoff's laws 2.7. Mesh and nodal analysis. 2.8. Bibliographic notes -- 3. Basoids. 3.1. Preliminaries. 3.2. Basoids of graphs. 3.3. Transitions from one basoid to another. 3.4. Minor with respect to a basoid. 3.5. Principal sequence 3.6. Principal minor and principal partition. 3.7. Hybrid rank and basic pairs of subsets. 3.8. Hybrid analysis of networks. 3.9. Procedure for finding an optimal basic pair. 3.10. Bibliographic notes -- 4. Pairs of Trees 4.1. Diameter of a tree. 4.2. Perfect pairs of trees. 4.3. Basoids and perfect pairs of trees. 4.4. Superperfect pairs of trees. 4.5. Unique solvability of affine networks. 4.6. Bibliographic notes 5. Maximally Distant Pairs of Trees. 5.1. Preliminaries. 5.2. Minor with respect to a pair of trees. 5.3. Principal sequence. 5.4. The principal minor. 5.5. Hybrid pre-rank and the principal minor 5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes |
| ctrlnum | (ZDB-20-CBO)CR9780511666391 (OCoLC)992910393 (DE-599)BVBBV043942157 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511666391 |
| format | Electronic eBook |
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| id | DE-604.BV043942157 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:18Z |
| institution | BVB |
| isbn | 9780511666391 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351126 |
| oclc_num | 992910393 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (x, 176 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in theoretical computer science |
| spelling | Novak, Ladislav 1950- Verfasser aut Hybrid graph theory and network analysis Ladislav Novak, Alan Gibbons Hybrid Graph Theory & Network Analysis Cambridge Cambridge University Press 1999 1 online resource (x, 176 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in theoretical computer science 49 Title from publisher's bibliographic system (viewed on 05 Oct 2015) 1. Two Dual Structures of a Graph. 1.1. Basic concepts of graphs. 1.2. Cuts and circs. 1.3. Cut and circ spaces. 1.4. Relationships between cut and circ spaces. 1.5. Edge-separators and connectivity 1.6. Equivalence relations among graphs. 1.7. Directed graphs. 1.8. Networks and multiports. 1.9. Kirchhoff's laws. 1.10. Bibliographic notes -- 2. Independence Structures. 2.1. The graphoidal point of view 2.2. Independent collections of circs and cuts. 2.3. Maximal circless and cutless sets. 2.4. Circ and cut vector spaces. 2.5. Binary graphoids and their representations. 2.6. Orientable binary graphoids and Kirchhoff's laws 2.7. Mesh and nodal analysis. 2.8. Bibliographic notes -- 3. Basoids. 3.1. Preliminaries. 3.2. Basoids of graphs. 3.3. Transitions from one basoid to another. 3.4. Minor with respect to a basoid. 3.5. Principal sequence 3.6. Principal minor and principal partition. 3.7. Hybrid rank and basic pairs of subsets. 3.8. Hybrid analysis of networks. 3.9. Procedure for finding an optimal basic pair. 3.10. Bibliographic notes -- 4. Pairs of Trees 4.1. Diameter of a tree. 4.2. Perfect pairs of trees. 4.3. Basoids and perfect pairs of trees. 4.4. Superperfect pairs of trees. 4.5. Unique solvability of affine networks. 4.6. Bibliographic notes 5. Maximally Distant Pairs of Trees. 5.1. Preliminaries. 5.2. Minor with respect to a pair of trees. 5.3. Principal sequence. 5.4. The principal minor. 5.5. Hybrid pre-rank and the principal minor 5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved Graph theory Network analysis (Planning) Graphentheorie (DE-588)4113782-6 gnd rswk-swf Netzwerkanalyse (DE-588)4075298-7 gnd rswk-swf Matroid (DE-588)4128705-8 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s Matroid (DE-588)4128705-8 s Netzwerkanalyse (DE-588)4075298-7 s 1\p DE-604 Gibbons, Alan Sonstige oth Erscheint auch als Druckausgabe 978-0-521-10659-7 Erscheint auch als Druckausgabe 978-0-521-46117-7 https://doi.org/10.1017/CBO9780511666391 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Novak, Ladislav 1950- Hybrid graph theory and network analysis 1. Two Dual Structures of a Graph. 1.1. Basic concepts of graphs. 1.2. Cuts and circs. 1.3. Cut and circ spaces. 1.4. Relationships between cut and circ spaces. 1.5. Edge-separators and connectivity 1.6. Equivalence relations among graphs. 1.7. Directed graphs. 1.8. Networks and multiports. 1.9. Kirchhoff's laws. 1.10. Bibliographic notes -- 2. Independence Structures. 2.1. The graphoidal point of view 2.2. Independent collections of circs and cuts. 2.3. Maximal circless and cutless sets. 2.4. Circ and cut vector spaces. 2.5. Binary graphoids and their representations. 2.6. Orientable binary graphoids and Kirchhoff's laws 2.7. Mesh and nodal analysis. 2.8. Bibliographic notes -- 3. Basoids. 3.1. Preliminaries. 3.2. Basoids of graphs. 3.3. Transitions from one basoid to another. 3.4. Minor with respect to a basoid. 3.5. Principal sequence 3.6. Principal minor and principal partition. 3.7. Hybrid rank and basic pairs of subsets. 3.8. Hybrid analysis of networks. 3.9. Procedure for finding an optimal basic pair. 3.10. Bibliographic notes -- 4. Pairs of Trees 4.1. Diameter of a tree. 4.2. Perfect pairs of trees. 4.3. Basoids and perfect pairs of trees. 4.4. Superperfect pairs of trees. 4.5. Unique solvability of affine networks. 4.6. Bibliographic notes 5. Maximally Distant Pairs of Trees. 5.1. Preliminaries. 5.2. Minor with respect to a pair of trees. 5.3. Principal sequence. 5.4. The principal minor. 5.5. Hybrid pre-rank and the principal minor 5.6. Principal partition and Shannon's game. 5.7. Bibliographic notes Graph theory Network analysis (Planning) Graphentheorie (DE-588)4113782-6 gnd Netzwerkanalyse (DE-588)4075298-7 gnd Matroid (DE-588)4128705-8 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4075298-7 (DE-588)4128705-8 |
| title | Hybrid graph theory and network analysis |
| title_alt | Hybrid Graph Theory & Network Analysis |
| title_auth | Hybrid graph theory and network analysis |
| title_exact_search | Hybrid graph theory and network analysis |
| title_full | Hybrid graph theory and network analysis Ladislav Novak, Alan Gibbons |
| title_fullStr | Hybrid graph theory and network analysis Ladislav Novak, Alan Gibbons |
| title_full_unstemmed | Hybrid graph theory and network analysis Ladislav Novak, Alan Gibbons |
| title_short | Hybrid graph theory and network analysis |
| title_sort | hybrid graph theory and network analysis |
| topic | Graph theory Network analysis (Planning) Graphentheorie (DE-588)4113782-6 gnd Netzwerkanalyse (DE-588)4075298-7 gnd Matroid (DE-588)4128705-8 gnd |
| topic_facet | Graph theory Network analysis (Planning) Graphentheorie Netzwerkanalyse Matroid |
| url | https://doi.org/10.1017/CBO9780511666391 |
| work_keys_str_mv | AT novakladislav hybridgraphtheoryandnetworkanalysis AT gibbonsalan hybridgraphtheoryandnetworkanalysis AT novakladislav hybridgraphtheorynetworkanalysis AT gibbonsalan hybridgraphtheorynetworkanalysis |