In-degree Distribution of Gradient Networks
In a gradient network, in-degree of a node i, ki (in) is the number of gradient edges pointing into i, and the in-degree distribution {ki (in)}
When the substrate G is random graph, and each pair of nodes is connected with probability P, the scalars hi are i.i.d. (independent identically distributed) the exact expression for R(l) is given by
In the limit N →∞ and P → 0, the degree distribution becomes the power law
This shows in this limit, the gradient network of random network is scale-free. If the subtstrate network G is scale-free, like BA model, then the gradient network also follow the power-law with the same exponent as those of G.
Read more about this topic: Gradient Network
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