Hi there,
i’m trying to understand the bfs properties(last one) which is described here
can anyone explain . thanks in advance 
Find the shortest path of even length from a source vertex s
to a target vertex t in an unweighted graph: For this, we must construct an auxiliary graph, whose vertices are the state (v,c), where v - the current node, c=0 or c=1 - the current parity. Any edge (a,b) of the original graph in this new column will t<urn into two edges ((u,0),(v,1)) and ((u,1),(v,0)). After that we run a BFS to find the shortest path from the starting vertex (s,0) to the end vertex (t,0).