Using the function from Project 15 and a fixed size, n, say 20, calculate the mean clustering coefficient (MCF) for networks with probabilities p = 0.0, 0.1, 0.2, ..., 1.0. For each probability, run the simulation a hundred times to obtain an average for MCF. Plot MCF versus p. Discuss the results.
Project 15
This project tests the observation that the mean clustering coefficient (MCF) for networks exhibiting the small-world property, such as most social net-works, is significantly higher than for random graphs (Mason and Verwoerd 2007). Using a realistic social network data set, calculate the MCF and the percentage (p) of Is, indicating edges, in its people-people connection ma-trix. Develop a function with parameters for a size, n, and a probability, p, to return a random n x n connection matrix, where p is the probability of 1 in a position. Calculate the MCF of a generated random graph for the number of people and the percentage of ones in the realistic social network. Run this simulation a number of times, say 100 to 1000 times, to obtain an average value for MCF, and compare the results with that of the realistic social network.