Dyadicity

Predictive Analytics using Networked Data in R

María Óskarsdóttir, Ph.D.

Post-doctoral researcher

Dyadicity

7 edges between green nodes

3 edges between green nodes

Dyadicity

Connectedness between nodes with the same label compared to what is expected in a random configuration of the network

Expected number of same label edges: ${{n_g}\choose{2}} \cdot p= \frac{n_g(n_g-1)}{2}\cdot p$
Example:
- Network with 9 white nodes, 6 green nodes, 21 edges, and connectance $p=0.2$
- Expected number of edges connecting two green nodes is 3 ($=\frac{6 \cdot 5 \cdot p}{2}$)
Dyadicity equals the actual number of same label edges divided by the expected number of same label edge
- $D=\frac{\textrm{number of same label edges}}{\textrm{expected number of same label edges}}$

Dyadicity

7 edges between green nodes

$D=7/3=2.33$

3 edges between green nodes

$D=3/3=1$

Types of Dyadicity

Three scenarios

$D>1 \Rightarrow$ Dyadic
$D\simeq 1\Rightarrow$ Random
$D<1\Rightarrow$ Anti-Dyadic

$D=2.33$

$D=1$

$D=0$

Dyadicity in the Network of Data Scientists

p <- 2 * 19 / (10 * 9)
expectedREdges <- 6 * 5 / 2 * p
expectedPEdges <- 4 * 3 / 2 * p

dyadicityR <- rEdges / expectedREdges
dyadicityP <- pEdges / expectedPEdges

dyadicityR

1.578947

dyadicityP

1.973684

Let's practice!

Predictive Analytics using Networked Data in R