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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 theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices. In an undirected simple graph of order n, the maximum degree of each vertex is n − 1 and the maximum size of the graph is ⁠ n(n − 1) / 2 ⁠.

  5. 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 ...

  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 distribution is very important in studying both real networks, such as the Internet and social networks, and theoretical networks.The simplest network model, for example, the (Erdős–Rényi model) random graph, in which each of n nodes is independently connected (or not) with probability p (or 1 − p), has a binomial distribution of degrees k:

  9. Coefficient of inbreeding - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_inbreeding

    An individual is said to be inbred if there is a loop in its pedigree chart. A loop is defined as a path that runs from an individual up to the common ancestor through one parent and back down to the other parent, without going through any individual twice. The number of loops is always the number of common ancestors the parents have.