From How to think in graphs: An illustrative introduction to Graph Theory and its applications by Vardan Grigoryan (vardanator)

In the contrary to the Facebook example, if Alice follows Bob on Twitter, that doesn’t require Bob to follow Alice back. So a “follow” relation must have a direction indicator, showing which vertex (user) has a directed edge (follows) to the other vertex.

From How to think in graphs: An illustrative introduction to Graph Theory and its applications by Vardan Grigoryan (vardanator)

Graphs can be directed and undirected, and that’s one of the interesting properties of graphs. You must’ve seen a popular Facebook vs Twitter example for directed and undirected graphs. A Facebook friendship relation may be easily represented as an undirected graph, because if Alice is a friend with Bob, then Bob must be a friend with Alice, too. There is no direction, both are friends with each other.

From How to think in graphs: An illustrative introduction to Graph Theory and its applications by Vardan Grigoryan (vardanator)

In his endeavor Euler showed that the possibility of a walk through graph (city) traversing each edge (bridge) one and only one time is strictly dependent on the degrees of vertices (lands). The path consisting of such edges called [in his honor] an Euler path. The length of an Euler path is the number of edges. Get ready for strict language.