Estimate the NDE and LLVE for the 36-node small-world grid network shown in Figure 3.8(a) of the textbook. For estimating the LLVE, the node locations can be assumed to be placed in suitable 2-D Cartesian coordinates. Compare the entropy values obtained for NDE and LLVE.
What will be an ideal response?
There is one typographical error in this exercise problem: Figure 3.8(a) should be
replaced with Figure 3.9(a).
To estimate LLVE, we always consider unit distance between a node-pair in the 36-node grid
network as shown in Figure 3.9(a). However, the length of a long-ranged link (LL) is the
hop distance between two nodes in the network. For example, the length of the LL between
nodes 11 and 34 is 5, and the length of the LL between nodes 1 and 22 is 6.
The entropy value with NDE is 3.5539.
The entropy value with LLVE is 2.2350.
Note that a regular grid, with unit distance between a nod-pair, has 0 network entropy value
when LLVE is concerned. With a few LLs (here 8 LLs), LLVE returns non-zero entropy value
because of the deviation in the average link length (i.e.,La) in the network. However, NDE
takes into account only the degree value for each node, in the network, to estimate network
entropy.
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