Assertion: graph | /r/HasProperty | connected
Facets:
value: fully
type: DEGREE
value: strongly
type: DEGREE
Source sentences:
text: If there is a path linking any two vertices in a graph, that graph is said to be connected.
text: For a directed graph, this means that the graph is strongly connected and every vertex has in-degree equal to the out-degree.
text: A graph is connected if any two vertices of the graph are connected by a path; while a graph is disconnected if at least two vertices of the graph are not connected by a path.
text: A graph is connected if there are paths containing each pair of vertices.
text: If a graph G is connected and locally finite, then it has a compact cover in which the set
text: A graph that is in one piece is said to be connected, whereas one which splits into several pieces is disconnected.
text: The vertex set (of an undirected graph) and the distance function form a metric space, if and only if the graph is connected.
text: A graph that is itself connected has exactly one component, consisting of the whole graph.
text: In most applications of this concept, it is restricted to embeddings with the property that each face is a topological disk; this constraint generalizes the requirement for planar graphs that the graph be connected.
text: In this context, it is common to assume that all graphs are connected, with self-loops and multiple edges allowed (that is, they are multigraphs rather than simple graphs); the contraction of a loop and the deletion of a cut-edge are forbidden operations.
text: A graph is connected if there is a path from every vertex to every other vertex.
text: If the graph is fully connected it requires storing 3,000,000 values.
text: Generally, we first have to build a graph by starting with a set of nodes and adding in any edges we need, and then we want to extract information from it, such as "Is this graph connected?