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Strongly Connected Components for Directed Graphs

Strongly Connected Components for Directed Graphs. Kelley Louie Credits: graphs by /demo/graphwin/graphwin. Overview. The following algorithm will determine if a directed graph contains strongly connected components: 1. perform depth first search and label vertices in post fix order

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Strongly Connected Components for Directed Graphs

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  1. Strongly Connected Componentsfor Directed Graphs Kelley Louie Credits: graphs by /demo/graphwin/graphwin

  2. Overview • The following algorithm will determine if a directed graph contains strongly connected components: • 1. perform depth first search and label vertices in post fix order • 2. compute reversed directed graph • 3. perform depth first search on reversed graph • 4. components of this forest are strongly connected components

  3. Depth First Search and Post Fix Order • Perform depth first search on the graph black - tree edge blue - cross edge orange - back edge • Label nodes in post fix order • note: start dfs at node 4 then node 9

  4. Reverse Directed Graph • Compute reversed directed graph (copy the graph but reverse the arrows)

  5. Depth First Search on Reversed Graph • Perform depth first search on reversed graph starting as highest post fix order vertex • continue until finished

  6. Strongly Connected Components • Components from the depth first search of the reversed graph compose the strongly connected components of the original graph

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