Average Watts-strogatz Clustering and Network Model IT Assignment Help

Assignment Task

Attempt the following questions:
a: Look at the descriptions (i) through (iv) of the network models (ignore v through vii) in section B and write a set of commands for your choice of two of these four networks. 
b: Network reciprocity R is defined as follows: where L is the total number of 1-step links i j in the network, and L? is the total number of pairs that have a link the total number of symmetric/undirected links. Write a command R[A] that calculates the network reciprocity of a network with adjacency matrix A.Generate two samples of networks, one sample of at least 50 draws for each network category you chose, with networks of N = 16 nodes and an average degree E {din + dout} ? 5, andanalyze the network reciprocity across each of the 2 samples, and check whether, in each of the samples, there is any relationship between R and one of the following network properties: 1) Newman Clustering, 2) Average Watts-Strogatz clustering
3) Assortativity. 
B: Average Watts-Strogatz clustering.
Suppose we have a network with adjacency matrix A and we compute the ATS by calculatin  and then setting all the diagonal elements to 0. This matrix then ‘counts’ the number of twostep connections between all node pairs j.

Attempt the following questions:

• Consider a node pair {i, j} for which (ATS)ij > 0 but Aji = 0,
• explain why this means there are unclosed triangles from i ? i via j, and
• write a command UnT[A] that calculates how many unclosed triangles there are in a network

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