LOCAL and CONGEST model in graph theory I am currently trying to understand a mathematical paper about graph theoretic concepts. In the abstract as well as in the introduction and through out the paper the "CONGEST" and "LOCAL" model is mentioned. I would like to ask if there is a clear definition to these terms?

Those are models of communication in distributed computation.

**The LOCAL model** :
Every vertex can send $poly(n)$ bits of information to each of its neighbors, each round.

**The CONGEST model** :
Every vertex can send $\log(n)$ bits of information to each of its neighbors, each round.

In both cases, the algorithm complexity is measured in the number of rounds it performs.