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Graph Theory Formulas
Browse 0 reviewed graph theory formulas with concrete inputs, outputs, calculations, applicability checks, and LaTeX.
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Graph Theory
Average Graph Degree
\bar d=\frac{2|E|}{|V|}Computes the mean degree of a finite undirected graph.
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Complete Graph Edge Count
|E(K_n)|=\frac{n(n-1)}{2}Counts the edges in a simple complete graph on n vertices.
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Degree from Adjacency Matrix
\deg(v_i)=\sum_j A_{ij}Computes a vertex degree by summing its row in a simple undirected graph adjacency matrix.
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Euler Formula for Planar Graphs
|V|-|E|+|F|=2Relates vertices, edges, and faces in a connected planar embedding.
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Handshake Lemma
\sum_{v\in V}\deg(v)=2|E|Relates the sum of all vertex degrees in a finite undirected graph to twice its edge count.
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Tree Edge Count
|E|=|V|-1States the edge count of a finite connected acyclic graph.
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