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  2. Loop (graph theory) - Wikipedia

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

    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 multiple edges between the same ...

  3. Reachability - Wikipedia

    en.wikipedia.org/wiki/Reachability

    In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s {\displaystyle s} can reach a vertex t {\displaystyle t} (and t {\displaystyle t} is reachable from s {\displaystyle s} ) if there exists a sequence of adjacent vertices (i.e. a walk ) which starts with s {\displaystyle s} and ends ...

  4. Graph theory - Wikipedia

    en.wikipedia.org/wiki/Graph_theory

    A loop is an edge that joins a vertex to itself. Graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for an undirected simple graph) or is incident on (for an undirected multigraph) {,} = {} which is not in {{,},}. To allow loops, the definitions must be expanded.

  5. Glossary of graph theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_graph_theory

    The transitive closure of a given directed graph is a graph on the same vertex set that has an edge from one vertex to another whenever the original graph has a path connecting the same two vertices. A transitive reduction of a graph is a minimal graph having the same transitive closure; directed acyclic graphs have a unique transitive reduction.

  6. Betweenness centrality - Wikipedia

    en.wikipedia.org/wiki/Betweenness_centrality

    The betweenness centrality for each vertex is the number of these shortest paths that pass through the vertex. Betweenness centrality was devised as a general measure of centrality: [1] it applies to a wide range of problems in network theory, including problems related to social networks, biology

  7. Component (graph theory) - Wikipedia

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

    In an empty graph, each vertex forms a component with one vertex and zero edges. [3] More generally, a component of this type is formed for every isolated vertex in any graph. [4] In a connected graph, there is exactly one component: the whole graph. [4] In a forest, every component is a tree. [5] In a cluster graph, every component is a ...

  8. Biological network - Wikipedia

    en.wikipedia.org/wiki/Biological_network

    One of the types of measures that biologists utilize is correlation which specifically centers around the linear relationship between two variables. [49] As an example, weighted gene co-expression network analysis uses Pearson correlation to analyze linked gene expression and understand genetics at a systems level. [ 50 ]

  9. Vertex (graph theory) - Wikipedia

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

    A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...