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  2. Connectivity (graph theory) - Wikipedia

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

    This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...

  3. k-vertex-connected graph - Wikipedia

    en.wikipedia.org/wiki/K-vertex-connected_graph

    A graph with connectivity 4. In graph theory, a connected graph G is said to be k-vertex-connected (or k-connected) if it has more than k vertices and remains connected whenever fewer than k vertices are removed. The vertex-connectivity, or just connectivity, of a graph is the largest k for which the graph is k-vertex-connected.

  4. Category:Graph connectivity - Wikipedia

    en.wikipedia.org/wiki/Category:Graph_connectivity

    Download as PDF; Printable version ... Connectivity (graph theory) 0–9. ... Balinski's theorem; Biconnected component; Biconnected graph; Bridge (graph theory) C ...

  5. Dynamic connectivity - Wikipedia

    en.wikipedia.org/wiki/Dynamic_connectivity

    In computing and graph theory, a dynamic connectivity structure is a data structure that dynamically maintains information about the connected components of a graph. The set V of vertices of the graph is fixed, but the set E of edges can change. The three cases, in order of difficulty, are:

  6. Robbins' theorem - Wikipedia

    en.wikipedia.org/wiki/Robbins'_theorem

    In graph theory, Robbins' theorem, named after Herbert Robbins (), states that the graphs that have strong orientations are exactly the 2-edge-connected graphs.That is, it is possible to choose a direction for each edge of an undirected graph G, turning it into a directed graph that has a path from every vertex to every other vertex, if and only if G is connected and has no bridge.

  7. Network neuroscience - Wikipedia

    en.wikipedia.org/wiki/Network_neuroscience

    The utilization of graph theory in neuroscience studies has been actively applied after the discovery of functional brain networks. In graph theory, an N × N adjacency matrix (also called a connection matrix) with the elements of zero or non-zero indicates the absence or presence of a relationship between the vertices of a network with N nodes.

  8. Betweenness centrality - Wikipedia

    en.wikipedia.org/wiki/Betweenness_centrality

    In graph theory, betweenness centrality is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph , there exists at least one shortest path between the vertices, that is, there exists at least one path such that either the number of edges that the path passes through (for unweighted graphs ...

  9. Strongly connected component - Wikipedia

    en.wikipedia.org/wiki/Strongly_connected_component

    The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex. If each strongly connected component is contracted to a single vertex, the resulting graph is a directed acyclic graph, the condensation of G.