Depth-first search marks a vertex when first reached, then recursively explores each still-unvisited neighbour before returning. To cover the whole graph, restart from every vertex not reached by earlier searches:
visit(v):
    visited[v] = true
    for w in adjacency[v]:
        if not visited[w]:
            visit(w)

for v in V:
    if not visited[v]:
        visit(v)
For a directed graph, use outgoing neighbours; for an undirected graph, use both incidences of each edge. Each vertex is discovered once and each stored incidence is inspected once. Thus with adjacency lists the running time is and the visited information and recursion stack use space. An adjacency matrix representation instead requires scanning possible neighbours per visited vertex, giving time.

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