Define Weakly Connected Graph. Want to thank TFD for its existence. Definition Weak Connectedness of a Directed GraphA directed graph is weakly connectedif the underlying undirected graph is connected.
This section describes the Weakly Connected Components WCC algorithm in the Neo4j Graph Data Science library. To solve this algorithm firstly DFS algorithm is used to get the finish time of each vertex now find the finish time of the transposed graph then the vertices are sorted in descending order by topological sort. The weakly connected components correspond closely to the concept of connected component in undirected graphs and the typical situation is similar.
The WCC algorithm finds sets of connected nodes in an undirected graph where all nodes in the same set form a connected component.
WCC is often used early in an analysis to understand the structure of a graph. This is exactly the same idea as in undirected graphs. A weakly connected graph can be thought of as a digraph in which every vertex is reachable from every other but not necessarily following the directions of the arcs. A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected undirected graph.
