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BUILT-IN MATHEMATICA SYMBOL
BreadthFirstScan
BreadthFirstScan[g, s, {"event1"->f1, "event2"->f2, ...}]
performs a breadth-first scan (bfs) of the graph g starting at the vertex s and evaluates 
whenever 
occurs.
BreadthFirstScan[g, {"event1"->f1, "event2"->f2, ...}]
performs a breadth-first scan of the whole graph g.
Details
- BreadthFirstScan[g, s, {...}] visits vertices in the graph g connected to the vertex s in breadth-first order.
- In breadth-first order, all vertices adjacent to the currently visited vertex are visited first.
- BreadthFirstScan[g, {...}] performs multiple breadth-first scans starting from the first vertex in the vertex list of g, and then starts from the first vertex in the vertex list that has not been visited, effectively scanning each connected component.
- BreadthFirstScan[g, ...] gives a list
representing a tree where 
is the predecessor of 
and where 
is the vertex list of g. - Events that provide access to vertex discovery include:
-
"DiscoverVertex" when vertices are discovered "UnvisitedVertex" when unvisited vertices are rediscovered "VisitedVertex" when visited vertices are rediscovered - "DiscoverVertex"->fd calls
when vertex u is discovered from visited vertex v at distance d from the start vertex s. - "UnvisitedVertex"->fru calls
when the unvisited vertex u is rediscovered from the visited vertex v. - "VisitedVertex"->frv calls
when the visited vertex u is rediscovered from the visited vertex v. - Events that provide access to vertex visits include:
-
"PrevisitVertex" before a vertex is visited "PostvisitVertex" after a vertex has been visited - "PrevisitVertex"->fs calls
before the vertex u has been visited. - "PostvisitVertex"->fe calls
after the vertex u has been visited. - A bfs-tree is the tree generated by the edges traversed during a breadth-first scan.
- Events that provide access to edge exploration from the visited vertex include:
-
"FrontierEdge" edge in the bfs-tree "CycleEdge" edge not in the bfs-tree - "FrontierEdge"->ffe calls
for an edge 
where the vertex v is being visited and u has not been discovered. Typically useful for scanning the bfs-tree. - "CycleEdge"->fce calls
for an edge 
where the vertex v is being visited and u has already been discovered. Typically useful for finding cycles or edges not in the bfs-tree. - For an undirected graph the edges used in the callbacks are taken to be undirected edges
.
New in 8
