Figure 5.

Degree correlations (A and B) and average path lengths (C and D) in random graphs with specified degree distributions (Poisson and exponential with mean degree = 5) compared to clustered random graphs with the same degree distributions and T = 0.5 generated by our algorithm (with the connectivity constraint), as well as the Volz [30]and Newman [20]algorithms (in A and B). The graphs present averages over 15 graphs generated by each algorithm. Our algorithm introduces fewer degree correlations than the alternatives, and the clustered graphs have only slightly higher average path lengths than their random counterparts: 4.05 for the Poisson random graphs versus 4.39 for the clustered graphs; and 3.95 for the exponential random graphs versus 4.14 for the clustered graphs.