So i'm currently reading a lot of things about graph NP-complete problems, and it seems that the goal of a lot of researchers is to find new results about their complexity, results like "independent set is 1.593 approximable for graphs which doesn't contains K4 K5 P3 as a minor" (this is probably a wrong result i just invented something which looks like a result we could find in a paper), approximation algorithms, parameterized complexity etc ...
But i'm wondering : what really is the goal to study independent set, vertex cover, hamiltonian circuit etc ... ? Do they have real case application ? Is there any software that uses independent set algorithms ?
Or is it only for the theory ? To discover something new in the P vs NP problems ?
To sum up : are NP-complete problems (and i'm particularly interested in NP-complete graph problems) useful in the reality ?
PS : sorry if the title may seem offensive, it is not, i know a lot of searchers study things which does not have much applications in reality, i want to know if it is the case for np-complete problems