The connected components
3 The connected components Molloy and Reed [1995] showed that for a random graph with vertices of degree i, where are non-negative values which sum to 1, the giant component emerges when So long as the maximum degree is less than They also show that almost surely there is no giant component when and maximum degree less than Here we compute Q for our graphs. We are thus led to consider the value which is a solution to If We first summarize the results here: 1. When the random graph a. s. has no giant component. When there is almost surely a unique giant component. 2. When almost surely the second largest components have size there is almost surely a component of size x. 3. When almost surely the second largest components are of size For any there is almost surely a component of size x. 4. When the second largest components are a. s. of size The graph is almost surely not connected. 5. When 0 <β<