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notes:net:sf [2015/07/16 21:32] (current)
vlado created
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 +====== Scale free networks ======
 +
 +Danes sem se odločil pogledati, kako je za dano porazdelitev z ustrezno kumulativno funkcijo.
 +
 +Naj bo dana porazdelitev  (p<sub>k</sub>). Tedaj definiramo zaporedje
 +
 +q<sub>k</sub> = ∑(i=k,∞) p<sub>i</sub>
 +
 +če za p<sub>k</sub> velja potenčni zakon  p<sub>k</sub> = c  k<sup>-α</sup>  velja tudi za  (q<sub>k</sub>)
 +
 +q<sub>k</sub> ~ ∫(k,∞) c  x<sup>-α</sup>  dx  ~  C  k<sup>-α + 1</sup>
 +
 +Torej moramo dobiti na sliki dve (skoraj) premici (npr. kot na {{notes:pics:sf.pdf}}).
 +<code>
 +setwd("C:/Users/batagelj/Documents/manuscripts/monika/zb/R")
 +F <- read.table("keywords_simple.vec", skip=1)$V1 
 +# F <- read.table("scaleFree.vec", skip=1)$V1 
 +T <- table(F) 
 +x <- as.numeric(names(T)); t <- as.vector(T)
 +n <- max(x); zx <- 1:n 
 +X <- numeric(n) 
 +X[x] <- t Z <- X[n:1] 
 +z <- cumsum(Z)[n:1] 
 +plot(zx,z,pch=16,cex=0.5,col='red',log="xy") 
 +points(x,t,pch=16,cex=0.5) 
 +</code>
 +
 +Če stvar narišemo za  keywords , je zaporedje  p  precej premično, zaporedje
 +q  pa močno odstopa od tega (slika {{notes:pics:keywords.pdf}}). Torej je brezlestvičnost
 +zaporedja  p  le navidezna.
  
notes/net/sf.txt · Last modified: 2015/07/16 21:32 by vlado
 
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