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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 ...
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points ), together with a set of unordered pairs of these ...
In computer science, directed graphs are used to represent knowledge (e.g., conceptual graph), finite-state machines, and many other discrete structures. A binary relation R on a set X defines a directed graph. An element x of X is a direct predecessor of an element y of X if and only if xRy.
For disconnected graphs, definitions vary: the diameter may be defined as infinite, or as the largest diameter of a connected component, or it may be undefined. diamond The diamond graph is an undirected graph with four vertices and five edges. diconnected Strong ly connected. (Not to be confused with disconnected) digon
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.
This definition is used effectively for disconnected graphs and allows to create convenient formulae for graph operations. For example: If graph G 1 + G 2 {\displaystyle G_{1}+G_{2}} is created by linking node p {\displaystyle p} of graph G 1 {\displaystyle G_{1}} to node q {\displaystyle q} of graph G 2 {\displaystyle G_{2}} then the combined ...
On the right side of the partition, all possible edges from top to bottom exist, forming a graph whose complement is disconnected. In graph theory, a skew partition of a graph is a partition of its vertices into two subsets, such that the induced subgraph formed by one of the two subsets is disconnected and the induced subgraph formed by the ...
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.