What is graph?
A graph is a set of nodes and that set must not be empty. The graph contains the following important components.
Start node: A set of initial nodes and that set must not be empty.
Final node: A set of final nodes and that set must not be empty.
Edges: A set of edges. Edge is a link of one node with another node.
Path : A path is a sequence of nodes.
Edge: Each pair of nodes is an edge
Length: The number of edges represents the length of the graph. Note that only one single node is a path of length 0
Subpath: A smaller subset path of a big superset path is subpath.
Reach: A reach is a subgraph that can be reached from nodes.
Example of Paths:
Following are some of the paths in the above-mentioned diagram.
[ 0, 3, 7 ], [ 1, 4, 8, 5, 1 ], [ 2, 6, 9 ]
Similarly, there are also some more possible paths in figure 2.
Example of Reach:
Following are some of the reach in the above-mentioned Figure 2.
Reach (0) = { 0, 3, 4, 7, 8, 5, 1, 9 }
This means that if we starts from node 0 then we can reach 3, we can reach,4 and similarly we can reach 7,8,5,1,9
Reach([2,6]) = {2, 6, 9}
This means that if we starts from node 0 and then after 0 if we read 6, then we can reach 9 only.