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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 ...
These algorithms find the minimum spanning forest in a possibly disconnected graph; in contrast, the most basic form of Prim's algorithm only finds minimum spanning trees in connected graphs. However, running Prim's algorithm separately for each connected component of the graph, it can also be used to find the minimum spanning forest. [9]
Build n copies of the star graph on 4 vertices. Denote the central vertex of each star A i and the outer vertices B i, C i and D i. This results in a disconnected graph on 4n vertices with 3n edges (A i – B i, A i – C i and A i – D i for 1 ≤ i ≤ n). Construct the n-cycle (B 1... B n). This adds n edges. Finally construct the 2n-cycle ...
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex cuts in the graph. An SPQR tree is a tree data structure used in computer science , and more specifically graph algorithms , to represent the triconnected components of a graph.
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.
A graph with three components. In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting ...
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.