- Example:
- Di-graph:
- Adjacency list representation:
- Adjacency matrix representation:
0 1 2 3 4 5 6 7 8 +- -+ | 0 1 0 1 0 0 0 0 0 | // 0 | 1 0 0 0 0 0 0 1 0 | // 1 | 0 0 0 0 0 1 0 0 0 | // 2 | 1 0 1 0 1 0 0 0 0 | // 3 M = | 0 0 0 0 0 0 0 0 1 | // 4 | 0 0 1 0 0 0 1 0 0 | // 5 | 0 0 0 0 0 0 0 0 0 | // 6 | 0 0 1 0 0 0 0 0 0 | // 7 | 1 0 0 0 0 0 0 0 0 | // 8 +- -+
- Di-graph:
- The DFS and
BFS
algorithms
are unaware (oblivious)
of the direction of the edges
- In fact, the adjacency list
and adjacency matrix are
di-graph representations:
- One undirected edge in the graph is represented by 2 "edges" in the adjacency list and adjacency matrix
- Hence:
- We can use the same old DFS and BFS algorithms to traverse di-graphs
- Traversal in directed and undirected graphs:
- The traversal of
a undirected graph from
a node x will
reach all nodes that
can are connected to x by a
path
- The traversal of a directed graph from a node x will reach only nodes that are reachable by a series of forward link
- The traversal of
a undirected graph from
a node x will
reach all nodes that
can are connected to x by a
path
- Example:
Forward path: 0 → 3 → 2
But starting at node 2, we cannot reach node 0
- Note:
- Directed edges are like one-way street....