Consider undirected networks without self-loops or duplicate links. Given N nodes and a variable number of...

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Consider undirected networks without self-loops or duplicate links. Given N nodes and a variable number of m edges, for what value of m do we obtain the largest diversity of networks? And for this m, how does the number of networks scale with N? (Hint: The so-called Stirling's approximation will be useful: I'(x + 1) = x! ~ √√2π·x²+¹/2.ex.) Consider undirected networks without self-loops or duplicate links. Given N nodes and a variable number of m edges, for what value of m do we obtain the largest diversity of networks? And for this m, how does the number of networks scale with N? (Hint: The so-called Stirling's approximation will be useful: I'(x + 1) = x! ~ √√2π·x²+¹/2.ex.)

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We have N nodes in the network Therefore the maximum number of edges in the net... View the full answer