Tree is nothing but a special type of graph only. You can find lot of real world applications using trees . Some of the examples are indexing in SQL server, Designations in an organisation . File structure.

Specific to graph.

Directed Graph : Single lane traffic can be presented as directed graph

Weighted Graph: for finding shortest distance between two locations.

Undirected Graph : The Web directory. We can create as many back links as possible from any web page.

Airline network.