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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. lambda-connectedness - Wikipedia

    en.wikipedia.org/wiki/Lambda-connectedness

    Such connected relations only describe either full connection or no connection. lambda-connectedness is introduced to measure incomplete or fuzzy relations between two vertices, points, human beings, etc. In fact, partial relations have been studied in other aspects. Random graph theory allows one to assign a probability to each edge of a graph ...

  5. 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.

  6. Algebraic connectivity - Wikipedia

    en.wikipedia.org/wiki/Algebraic_connectivity

    An example graph, with 6 vertices, diameter 3, connectivity 1, and algebraic connectivity 0.722 The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of G. [1]

  7. Weighted network - Wikipedia

    en.wikipedia.org/wiki/Weighted_network

    A weighted network is a network where the ties among nodes have weights assigned to them. A network is a system whose elements are somehow connected. [1] The elements of a system are represented as nodes (also known as actors or vertices) and the connections among interacting elements are known as ties, edges, arcs, or links.

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  9. Connectedness - Wikipedia

    en.wikipedia.org/wiki/Connectedness

    For example, a graph is said to be connected if each pair of vertices in the graph is joined by a path. This definition is equivalent to the topological one, as applied to graphs, but it is easier to deal with in the context of graph theory. Graph theory also offers a context-free measure of connectedness, called the clustering coefficient.