Posted: February 10th, 2017

Speculate on how many connected components a random graph might have if the likelihood of an edge (v1,v2) being in the set E is 50%. Do you think the number of components would depend on the size of the vertex set V? Explain why or why not.

Random graphs are a fascinating subject of applied and theoretical research. These can be generated with a fixed vertex set V and edges added to the edge set Ebased on some probability model, such as a coin flip. Speculate on how many connected components a random graph might have if the likelihood of an edge (v1,v2) being in the set E is 50%. Do you think the number of components would depend on the size of the vertex set V? Explain why or why not.