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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. 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).

  5. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    This type of mapping between graphs is the one that is most commonly used in category-theoretic approaches to graph theory. A proper graph coloring can equivalently be described as a homomorphism to a complete graph. 2. The homomorphism degree of a graph is a synonym for its Hadwiger number, the order of the largest clique minor. hyperarc

  6. Regular graph - Wikipedia

    en.wikipedia.org/wiki/Regular_graph

    In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [1]

  7. Eulerian path - Wikipedia

    en.wikipedia.org/wiki/Eulerian_path

    Every vertex of this graph has an even degree. Therefore, this is an Eulerian graph. Following the edges in alphabetical order gives an Eulerian circuit/cycle. In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices).

  8. Network motif - Wikipedia

    en.wikipedia.org/wiki/Network_motif

    Network motifs are recurrent and statistically significant subgraphs or patterns of a larger graph.All networks, including biological networks, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as graphs, which include a wide variety of subgraphs.

  9. Biological network - Wikipedia

    en.wikipedia.org/wiki/Biological_network

    In biology, pairwise interactions have historically been the focus of intense study. With the recent advances in network science , it has become possible to scale up pairwise interactions to include individuals of many species involved in many sets of interactions to understand the structure and function of larger ecological networks . [ 29 ]