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Concept
Graph traversal
Summary
In computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph. Such traversals are classified by the order in which the vertices are visited. Tree traversal is a special case of graph traversal.
Unlike tree traversal, graph traversal may require that some vertices be visited more than once, since it is not necessarily known before transitioning to a vertex that it has already been explored. As graphs become more dense, this redundancy becomes more prevalent, causing computation time to increase; as graphs become more sparse, the opposite holds true.
Thus, it is usually necessary to remember which vertices have already been explored by the algorithm, so that vertices are revisited as infrequently as possible (or in the worst case, to prevent the traversal from continuing indefinitely). This may be accomplished by associating each vertex of the graph with a "color" or "visitation" state during the traversal, which is then checked and updated as the algorithm visits each vertex. If the vertex has already been visited, it is ignored and the path is pursued no further; otherwise, the algorithm checks/updates the vertex and continues down its current path.
Several special cases of graphs imply the visitation of other vertices in their structure, and thus do not require that visitation be explicitly recorded during the traversal. An important example of this is a tree: during a traversal it may be assumed that all "ancestor" vertices of the current vertex (and others depending on the algorithm) have already been visited. Both the depth-first and breadth-first graph searches are adaptations of tree-based algorithms, distinguished primarily by the lack of a structurally determined "root" vertex and the addition of a data structure to record the traversal's visitation state.
Note. — If each vertex in a graph is to be traversed by a tree-based algorithm (such as DFS or BFS), then the algorithm must be called at least once for each connected component of the graph.
Official source
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