how a graph can be implemented using adjacency lists/sets. How does it work for directed graphs? Undirected graphs? Weighted graphs?

Question

Could you please give me some clue that how a graph can be implemented using adjacency lists/sets and How does it work for directed graphs? Undirected graphs? Weighted graphs?

Answer 1

Consider a directed acyclic graph like this:

1->2 
1->3 
2->4 
2->5 
3->6 
3->7

Another way to view it is:

        1
      /   \
    2       3
  /   \   /   \
 4     5 6     7

This is really just a small binary tree. An adjacency list representation looks like:

1 -> {2, 3}
2 -> {4, 5}
3 -> {6, 7}

So consider that this could be a HashMap of Integers that point to Sets of Integers.

Now consider that the original graph is undirected, in other words there are parent pointers.

1<->2
1<->3
2<->4
2<->5
3<->6
3<->7

Now the representation needs more entries:

1 -> {2, 3}
2 -> {1, 4, 5}
3 -> {1, 6, 7}
4 -> {2}
5 -> {2}
6 -> {3}
7 -> {3}

Lets return to the directed version of the graph and weight it:

The weights are the first entry in the tuple and the child is the second entry. So it looks like
Parent->(Weight, Child) .

1->(.9,2) 
1->(.1,3) 
2->(.9,4) 
2->(.1,5) 
3->(.5,6) 
3->(.5,7)

So 90% of the time we go from 1->2 then 90% of the time that we are at 2 we will go 2->4 .

The representation can look very similar to the directed graph:

1 -> {(.9,2), (.1,3)}
2 -> {(.9,4), (.1,5)}
3 -> {(.5,6), (.5,7)}

Hope this helps.