If you look in the earth, not only earth, the whole universe can be viewed as a set of vertices and edges. From a tiny sub atomic particles to the gigantic universe graph plays a major role. Take yourself, see your blood vessels/nerves and major organs it's a graph. Obviously travelling form a graph. In communication field it has a strong role (Facebook friends, twitter followers, mobile and landline connections, Internet, wireless network). Even Time can be viewed as a graph.. If humans serve as a model of graph then obviously the robots too.. Think about the constellations.. Computer graphics is based on this only..
In simple words you can conceive everything as a graph since every object is made by vertices connected by edges.. The set of objects will serve as a vertices and there are corresponding features serves as a edges forming a graphical system..
Graphs are nothing but connected nodes(vertex). So any network related, routing, finding relation, path etc related real life applications use graphs.
> Connecting with friends on social media, where each user is a vertex, and when users connect they create an edge.
> Using GPS/Google Maps/Yahoo Maps, to find a route based on shortest route.
> Google, to search for webpages, where pages on the internet are linked to each other by hyperlinks; each page is a vertex and the link between two pages is an edge.
> On eCommerce websites relationship graphs are used to show recommendations.
> Graph theoretical concepts are widely used in Operations Research.
> Similarly, graph theory is used in sociology for example to measure actors prestige or to explore diffusion mechanisms.
Sources: Internet
