The clique problem instead asks: Given a social network, does it contain a group of a desired number of people who are all mutual friends? Both problems are NP-complete, meaning we don’t know ...

Typical problems: • The clique problem. Imagine a graph with edges and nodes — for example, a graph where nodes are individuals on Facebook and two nodes are connected by an edge if they’re “friends.” ...

And thus far, no algorithm to efficiently solve the clique problem has been discovered. Or, for that matter, to solve any of its NP-complete siblings, which is why most people do think that P ≠ NP.

Crisis Text Line helps teenagers through academic stress, clique problems at school and more serious issues like depression and suicidal thoughts. A couple of years ago, a new service called ...