Static edge voting models

Voting to the Link: a Static Network Formation Model

“…In this paper we continued and extended our preliminary work [12] about static edge voting models. In Section 2 started with reviewing the properties of inhomogeneous random graphs (IRG), because IRGs are our basic tool, and proved a corollary of the Chernoff-bounds what we can use to bound the probability that the degree of a fixed node is below or above of a given D value.…”

“…Networks generated by the BA model show power-law degree distribution. In this paper we continue and extend the work on static edge voting models [12]. The structure of this paper is as follows: after an introduction to the necessary notions and definitions, in Section 2 we turn to the Inhomogeneous Random Graphs.…”

“…In our preliminary paper [12] we have formalized the following proposition, and the proof is also given there. This is not a new theorem, but only the reformulation of the Chernoff bound [9] for the case of inhomogeneous random graphs.…”

“…Corollary 1 is a less strict, but easier to use theorem when L(D) < 1 holds. In ref [12], we showed that we can find an approximation of the degree distribution of node i with the N (µ, σ ) Gauss distribution, setting the parameters to µ = E[d i ] = ∑ j∈V i p i j and σ 2 = Var[d i ] = ∑ j∈V i p i j (1 − p i j ). The Lyapunov variant of the central limit theorem [14] gives the theoretical background for this.…”

“…Consider the case when V ab ∼ Poisson (λ i ) if a = b and a ∈ S i and the edge probability function is given as s(x) = 1 − e −λ x , where λ is the control parameter. We have shown [12] that the probability of the {a, b} edge is…”