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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 ...
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.
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 ...
As a physical system with graph-like properties, [6] a large-scale brain network has both nodes and edges and cannot be identified simply by the co-activation of brain areas. In recent decades, the analysis of brain networks was made feasible by advances in imaging techniques as well as new tools from graph theory and dynamical systems.
Equivalently, the connectivity of a graph is the greatest integer k for which the graph is k-connected. While terminology varies, noun forms of connectedness-related properties often include the term connectivity. Thus, when discussing simply connected topological spaces, it is far more common to speak of simple connectivity than simple ...
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e., the nodes are located in a space equipped with a certain metric.
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.
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.