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  2. Loop (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Loop_(graph_theory)

    A graph with a loop on vertex 1. In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing ...

  3. Degree (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Degree_(graph_theory)

    The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the graph.) A sequence which is the degree sequence of some simple ...

  4. Graph (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Graph_(discrete_mathematics)

    The degree or valency of a vertex is the number of edges that are incident to it; for graphs with loops, a loop is counted twice. In a graph of order n, the maximum degree of each vertex is n − 1 (or n + 1 if loops are allowed, because a loop contributes 2 to the degree), and the maximum number of edges is n(n − 1)/2 (or n(n + 1)/2 if loops ...

  5. Forbidden graph characterization - Wikipedia

    en.wikipedia.org/wiki/Forbidden_graph...

    Loops, pairs of parallel edges, and cycles of all lengths Subgraph Definition A loop (for multigraphs) or triangle K 3 (for simple graphs) Graph minor Definition Linear forests [A loop / triangle K 3 (see above)] and star K 1,3: Graph minor Definition Claw-free graphs: Star K 1,3: Induced subgraph Definition Comparability graphs: Induced subgraph

  6. Bipartite graph - Wikipedia

    en.wikipedia.org/wiki/Bipartite_graph

    The degree sequence of a bipartite graph is the pair of lists each containing the degrees of the two parts and . For example, the complete bipartite graph K 3,5 has degree sequence (,,), (,,,,). Isomorphic bipartite graphs have the same degree sequence. However, the degree sequence does not, in general, uniquely identify a bipartite graph; in ...

  7. Degree matrix - Wikipedia

    en.wikipedia.org/wiki/Degree_matrix

    In an undirected graph, this means that each loop increases the degree of a vertex by two. In a directed graph, the term degree may refer either to indegree (the number of incoming edges at each vertex) or outdegree (the number of outgoing edges at each vertex).

  8. Degree distribution - Wikipedia

    en.wikipedia.org/wiki/Degree_distribution

    The degree of a node in a network (sometimes referred to incorrectly as the connectivity) is the number of connections or edges the node has to other nodes. If a network is directed, meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of ...

  9. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    k-degenerate graphs have also been called k-inductive graphs. degree 1. The degree of a vertex in a graph is its number of incident edges. [2] The degree of a graph G (or its maximum degree) is the maximum of the degrees of its vertices, often denoted Δ(G); the minimum degree of G is the minimum of its vertex degrees, often denoted δ(G).