As a standard consequence of the above random degree theory, we can formulate: (Random Schauder fixed point theorem).
We presented four neighbor selection schemes (random, degree, propagation-weight, and hybrid selection) and explored their feasibility.
Given the specific degree density μ(d=i), the encoding process will be relatively straightforward, which mainly involves the following three steps: 1. select a random degree according to the distribution, i.e., d∼μ(d=i); 2.
select a random degree according to the distribution, i.e., d∼μ(d=i); choose d distinct neighbors around the current input bit b k in a uniform manner, which are denoted by (b_{k}^{(1)}, b_{k}^{(2)},ldots, b_{k}^{(d)}); calculate the exclusive-OR of the d-neighbors and finally output the encoder symbol.
The model shows that local webs with non-random degree distributions can arise from randomly structured source webs.
Nevertheless, some topological characteristics of the graphs representing the networks - namely non-random degree distribution and high clustering coefficient - are shared by networks of distantly related organisms.
We developed additional permutation tests allowing for random node degrees in the network and found the permutation tests conserving aspects of the network topology to be more stringent in assessing the statistical significance of our observations.
Instead of the deterministic topological degree, we use here the random topological degree presented in Section 9.
The degree distribution, usually denoted by P k), is the probability that a vertex chosen uniformly at random has degree k, or equivalently, the fraction of vertices in the network with degree k.
