Watts and Strogatz proposed a hybrid model that contains typical links of vertices near each other (people know their geographic neighbors), plus some random long-range connection links. Plot the effect of adding random edges to an \(n\)-by- \(n\) grid graph on the average path length and on the cluster coefficient, for \(n=100\). Do the same for \(k\)-ring graphs on \(V\) vertices, for \(V=10,000\) and various values of \(k\) up to \(10 \log V\).

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6-by-6 grid graph