The notion of "reachability" boils down to answering the question whether a vertex u can be reached from a source vertex s.
To answer this question, use a depth first search. See Graphs/DFS.
The notion of the shortest path from a vertex s to a vertex u is answered with breadth first search. See Graphs/BFS.
Graphsnotes on graph theory, graph implementations, and graph algorithms
Part of Computer Science Notes
Series on Data Structures
Flags · Template:GraphsFlagBase · e