Recall the most basic gf g0x p k xk k and the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Recall prob of following random edge to node of degree k : qk = kPk / k kPk = kPk / k . • Define a corresponding GF called G1(x): G1(x) = = q k xk k kPk xk / k k d = x dx ( d Pk xk )/ dx G0(x) k d d = x dx G0(x)/ dx G0(x) x=1 x=1 ≡ xG0(x)/G0(1). • (Recall the most basic GF: G0(x) = P k xk ) k and the distribution of the sum of the sizes of the k components is generated by H1 (as previously explained for the sum of degrees), i.e. H1(x), Generating kfunction for size S ) · x S = ( H1 (x ))component Prob(union of components has distribution in k . (A2.8) S sizes reached by following random edge A B H1(x) = xq0 + xq1H1(x) + xq2[H1(x)]2 + xq3[H1(x)]3 · · · (A self-consistency equation) Fig. A2.1. Diagrammatic visualization of property, (A2.9) random variable (Note here we used the “Powers”(A) Equation that a and (B) Equation (A2.10). Each square corresponds to an arbitrary tree-like cluster, while the kcircle is a node of the network. summed over m independent realizations of th...
View Full Document

This document was uploaded on 03/12/2014 for the course CSCI 289 at UC Davis.

Ask a homework question - tutors are online