Heterophilicity

Predictive Analytics using Networked Data in R

María Óskarsdóttir, Ph.D.

Post-doctoral researcher

Heterophilicity

4 cross label edges

11 cross label edges

Predictive Analytics using Networked Data in R

Heterophilicity

Connectedness between nodes with different labels compared to what is expected for a random configuration of the network

  • Expected number of cross label edges $=n_w n_g p$
  • Example:
    • Network with 9 white nodes, 6 green nodes, 21 edges, and connectance $p=0.2$
    • Expected number of cross label edges is 11 ($=9\cdot 6\cdot p$)
  • Heterophilicty equals the actual number of cross label edges divided by the expected number of cross label edges
    • $H=\frac{\textrm{number of cross label edges}}{\textrm{expected number of cross label edges}}$
Predictive Analytics using Networked Data in R

Heterophilicity

15 cross label edges

  • $H=15/11=1.39$

11 cross label edges

  • $H=11/11=1.02$
Predictive Analytics using Networked Data in R

Types of Heterophilicity

Three scenarios

  1. $H>1 \Rightarrow$ Heterophilic
  2. $H\simeq 1\Rightarrow$ Random
  3. $H<1\Rightarrow$ Heterophobic

$H=1.39$

$H=1.02$

$H=0.37$

Predictive Analytics using Networked Data in R

Heterophilicity in the network of data scientists

p<-2*19/(10*9)
m_rp<-6*4*p

H_rp<-edge_rp/m_rp

H_rp

0.3947368
Predictive Analytics using Networked Data in R

Let's practice!

Predictive Analytics using Networked Data in R

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