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The 27 pages that link to Degree (graph theory), each with the reason it gives.

• Graph theoryRelated: Vertex degrees capture local structure and support results such as the handshaking lemma.

• Complete graphRelated: Every vertex in a complete graph on n vertices has degree n−1.

• Graph (discrete mathematics)Related: Degree summarizes how many connections meet at each vertex.

• Edge (graph theory)Related: Counting incident edges measures how many connections meet at a vertex.

• Vertex (graph theory)Related: Degree measures how many direct connections a vertex has.

• MultigraphRelated: Parallel edges contribute separately to a vertex’s degree.

• Tree (graph theory)Related: Vertex degrees in a finite tree sum to twice its number of edges.

• Vertex (geometry)Related: Degree measures how many connections meet at a graph vertex.

• Edge coloringRelated: Edges incident to a high-degree vertex must all receive distinct colors.

• Graph isomorphismRelated: An isomorphism preserves every vertex's degree, providing a quick necessary test.

• Simple graphRelated: In a simple graph, a vertex can be adjacent to each other vertex at most once.

• Line graphRelated: An original vertex of degree d induces a clique of d line-graph vertices.

• Adjacency listRelated: In a simple undirected graph, a vertex's list length equals its degree.

• Network scienceBroader topic: Degree measures how many direct connections each network node has.

• Path graphRelated: Interior vertices have degree two, while the endpoints have degree one.

• Eulerian pathRelated: The parity of vertex degrees gives a simple test for Eulerian paths.

• Undirected graphRelated: Degree counts how many edge-ends meet at each vertex.

• Hamiltonian pathRelated: Degree conditions can rule out Hamiltonian paths or help establish their existence.

• Handshaking lemmaBroader topic: Summing this quantity over all vertices counts every edge endpoint.

• Seven Bridges of KönigsbergRelated: Each landmass’s degree counts how many bridges meet it.

• Brooks' theoremRelated: The maximum of these vertex degrees determines the theorem's bound.

• Regular graphRelated: A graph is regular precisely when every vertex has equal degree.

• Degree matrixRelated: Each diagonal entry records the degree of one vertex.

• Cayley's formulaRelated: A vertex appears in the Prüfer sequence exactly its degree minus one times.

• Edge contractionRelated: The merged vertex's degree depends on the endpoint degrees and shared incident edges.

• Laplacian matrixRelated: Each diagonal entry of the Laplacian records a vertex’s degree.

• Erdős–Gyárfás conjectureRelated: Minimum degree three is the hypothesis that drives the conjecture.