How can i know reachablity of A* algorithm on a graph? -

i got data set of graph.

then have distance between city , b.

how can know reachablity of route b ?

do have search reachable cities a*?

i think needs time.

if want know if arbitrary node reachable arbitrary node, yes, need search graph. yes, means end traversing every node on graph. yes, if have huge number of nodes, slow. life tough.

if need many such reachability checks, might worth pre-process graph, , store reachability information can used faster lookups. information take lot of space, though use secondary storage (i.e. hard drive).