In algebraic topology and graph theory, graph homology describes the homology groups of a graph, where the graph is considered as a topological space....

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...

Every covering space projecting to a graph is also a graph. Graph homology Topological graph theory Nielsen–Schreier theorem, whose standard proof makes...

2032324100, PMC 218723, PMID 14517352. Sugihara, George (1984), "Graph theory, homology and food webs", in Levin, Simon A. (ed.), Population Biology, Proc...

Sequence graph, also called an alignment graph, breakpoint graph, or adjacency graph, are bidirected graphs used in comparative genomics. The structure...

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,...

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...

invariant. In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological algebra. The Euler characteristic χ was...

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...

{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...