Why are directed graphs important?
Recalling that a directed graph is a graph where the edges have an associated direction with them. 

Using a directed graph you can represent asymmetrical relationships between nodes, while in undirected graph we can represent only symmetrical relationships.

Practically, using a directed graph you can represent:


Road networks (using a directed graph you can represent streets'  direction);
hyperlinks connecting web pages;
dependencies in software modules;
prey-predator relationships;
deterministic finite automaton.


Besides these classical examples, you can depict many other real-world scenarios (financial trade, scheduling, infectious disease, citation, control flow, etc) that needs an ordered relationship [1].