(Download dataset ca-GrQe.txt.gz from http://snap.stanford.eduidata/ca-GrQc.txt.gz.) The Stanford Large Network Dataset Collection stores the General Relativity and Quantum Cosmology collaboration network dataset with "scientific collaborations between authors papers submitted to General Relativity and Quantum Cosmology category" (SNAP 2012; ca-GrQc 2012). In this undirected graph, if authors i and j coauthored a paper, an edge exists between nodes i and j. For each of the following parts, calculate the metric, answer the indicated questions, and discuss the results and meaning of the metric in the context of the problem.

a. For this dataset, graph the degree distribution and determine a function that fits this distribution. Is the network scale free? If so, determine the largest hubs.

b. Find a minimal dominating set.

c. Calculate the mean clustering coefficient.

d. Determine the numbers of nodes and edges in the largest connected component.

e. Find the mean shortest-path length and the diameter (see Module 13.5, "The Next Flu Pandemic-Old Enemy, New Identity, Project 2). Does this network exhibit the small-world property?