connected graph definition in data structure
What is the difference between a connected graph and a spanning tree?
A connected graph is a graph in which there is always a path from a vertex to any other vertex. A spanning tree is a sub-graph of an undirected connected graph, which includes all the vertices of the graph with a minimum possible number of edges. If a vertex is missed, then it is not a spanning tree.
What is a connected component in an undirected graph?
A connected component or simply component of an undirected graph is a subgraph in which each pair of nodes is connected with each other via a path. Let’s try to simplify it further, though. A set of nodes forms a connected component in an undirected graph if any node from the set of nodes can reach any other node by traversing edges.
What is a graph based on?
One node is connected with another node with an edge in a graph. The graph is a non-linear data structure consisting of nodes and edges and is represented by G ( V, E ), where V stands for the set of vertices and E stands for the set of edges. The graphs are divided into various categories: directed, undirected, weighted and unweighted, etc.
What does connected mean in graph theory?
Most commonly in graph theory it is implied that the graphs discussed are finite. If the graphs are infinite, that is usually specifically stated. In an undirected graph, an unordered pair of vertices {x, y} is called connected if a path leads from x to y. Otherwise, the unordered pair is called disconnected .
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