Can someone explain Breadth-first search to solve the below kind of problems 
I need to find all the paths between 4 and 7
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You look at all the nodes adjacent to your start node. Then you look at all the nodes adjacent to those (not returning to nodes you’ve already looked at). Repeat until satisfying node found or no more nodes.
For the kind of problem you indicate, you use the process described above to build a set of paths, terminating any that arrive at the desired destination node, and when your graph is exhausted, the set of paths that so terminated is your solution set.