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A graph with 16 vertices and six bridges (highlighted in red) An undirected connected graph with no bridge edges. In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph's number of connected components. [1] Equivalently, an edge is a bridge if and only if it is not contained in any cycle.
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 ...
A directed graph or digraph is a graph in which edges have orientations. In one restricted but very common sense of the term, [5] a directed graph is an ordered pair = (,) comprising: , a set of vertices (also called nodes or points);
A biconnected undirected graph is a connected graph that is not broken into disconnected pieces by deleting any single vertex (and its incident edges).. A biconnected directed graph is one such that for any two vertices v and w there are two directed paths from v to w which have no vertices in common other than v and w.
DOT tutorial and specification. Drawing graphs with dot; Node, Edge and Graph Attributes; Node Shapes; Gallery of examples; Graphviz Online: instant conversion and visualization of DOT descriptions; Boost Graph Library; lisp2dot or tree2dot: convert Lisp programming language-like program trees to DOT language (designed for use with genetic ...
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
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 ...
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 ...