In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space....
13 KB (2,216 words) - 11:16, 7 May 2024
probably the simplest homology theory to use is graph homology, which could be regarded as a 1-dimensional special case of simplicial homology, the latter of...
54 KB (8,218 words) - 14:50, 22 August 2024
Every covering space projecting to a graph is also a graph. Graph homology Topological graph theory Nielsen–Schreier theorem, whose standard proof makes...
4 KB (510 words) - 06:55, 21 February 2024
2032324100, PMC 218723, PMID 14517352. Sugihara, George (1984), "Graph theory, homology and food webs", in Levin, Simon A. (ed.), Population Biology, Proc...
20 KB (2,496 words) - 08:26, 28 December 2023
Sequence graph, also called an alignment graph, breakpoint graph, or adjacency graph, are bidirected graphs used in comparative genomics. The structure...
5 KB (695 words) - 15:43, 30 April 2024
Cycle space (category Algebraic graph theory)
of the graph. The same space can also be described in terms from algebraic topology as the first homology group of the graph. Using homology theory,...
18 KB (2,511 words) - 12:40, 14 June 2024
Betti number (category Graph invariants)
they are all finite. The nth Betti number represents the rank of the nth homology group, denoted Hn, which tells us the maximum number of cuts that can be...
16 KB (2,508 words) - 10:59, 28 January 2024
Euler characteristic (category Topological graph theory)
invariant. In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological algebra. The Euler characteristic χ was...
29 KB (3,445 words) - 14:53, 17 June 2024
Chain complex (section Singular homology)
included in the kernel of the next. Associated to a chain complex is its homology, which describes how the images are included in the kernels. A cochain...
13 KB (2,029 words) - 20:38, 17 December 2023
{rank} H_{1}(G,t),} which is read as "the rank of the first homology group of the graph G relative to the terminal nodes t". This is a technical way...
23 KB (2,912 words) - 14:58, 1 May 2024