The distribution of shortest path lengths in the corded directed node-duplication network is a convolution of the seed distribution with Poisson terms, and its mean distance grows logarithmically with network size while the connected fraction vanishes.
Milgram, Psychology Today 1, 61 (1967)
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Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication
The distribution of shortest path lengths in the corded directed node-duplication network is a convolution of the seed distribution with Poisson terms, and its mean distance grows logarithmically with network size while the connected fraction vanishes.