[PDF] connected graph definition algorithms

A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair of vertices. An undirected graph that is not connected is called disconnected.
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  • What is a connected graph?

    A graph is a connected graph if, for each pair of vertices, there exists at least one single path which joins them.
    A connected graph may demand a minimum number of edges or vertices which are required to be removed to separate the other vertices from one another.

  • What is connected component algorithm?

    Connected components are the set of its connected subgraphs.
    Two nodes belong to the same connected component when there exists a path (without considering the direction of the edges) between them.
    Therefore, the algorithm does not consider the direction of edges.

  • What is connected component algorithm?

    A simple idea is to use a all pair shortest path algorithm like Floyd Warshall or find Transitive Closure of graph.
    Time complexity of this method would be O(v3).
    We can also do DFS V times starting from every vertex.
    If any DFS, doesn't visit all vertices, then graph is not strongly connected.

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