No, this statement is true for every graph that doesn't have constant degree. It's not really to do with random graphs. Rather it's the fact that a random neigh

No, this statement is true for every graph that doesn't have constant degree. It's not really to do with random graphs. Rather it's the fact that a random neighbor of a random node draws from a different distribution than a random node, and the former distribution puts more mass on nodes of higher degree.