connected graph

connected graph

[kə′nek·təd ′graf]
(mathematics)
A graph in which each pair of points is connected by a path.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

connected graph

(mathematics)
A graph such that there is a path between any pair of nodes (via zero or more other nodes).

Thus if we start from any node and visit all nodes connected to it by a single edge, then all nodes connected to any of them, and so on, then we will eventually have visited every node in the connected graph.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in periodicals archive ?
Let G = (V, E) be a connected graph. We define the distance as the minimum length of path connecting vertices u and v in G, denoted by d(u, v).
A connected graph has excess if it has more edges than vertices.
Let G be a simple connected graph with vertex set V(G) and edge set E(G).
Furthermore, if each [G.sub.i] with i = 1, 2 is a connected graph in Definition 4, and the TOE-source [G.sub.1] is a bipartite connected graph having its own bipartition ([X.sub.1], [Y.sub.1]) and a labelling f satisfying Definition 2, we call the 2-identification graph G = [[circle dot].sub.2] <[G.sub.1], [G.sub.2]> a set-ordered twin odd-elegant graph (So-TOE-graph) and f a set-ordered twin odd-elegant labelling (So-TOE-labelling).
For a connected graph, the Laplacian matrix L is symmetric and positive semi definite.
They also recognize graphical properties that assuring unique localizability, and proposed an approach G2 to make the two-connected graph localizable and a G3 approach to obtain a trilateration graph based on a connected graph. These two approaches treat all vertices in the graph as complete, which is more coarse-grained than LAL.
Given a connected graph G = (V, E) and a positive weight function w defined on E, then any w-minimum cut is a connected sides cut of G.
In this paper, the undirected and connected graph G will be considered, where its L is positive semidefinite and its eigenvalues are presented by 0 = [[lambda].sub.1] < [[lambda].sub.2] [less than or equal to] ...
We examined both tweets and users in order to create a connected graph from them with links between user-user, user-tweet and tweet-tweet elements.
All graphs considered in this paper are simple connected graph without loops and parallel link.
A connected graph G is said to be double-[psi]-critical if each edge of G is double-[psi]-critical.
This notion does not depend on [x.sub.0], and when (X, d) is a connected graph with graph distance this notion is equivalent to the transience of the usual random walk on this graph (Proposition 2.2).

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