assort {streamDAG} | R Documentation |
Assortativity
Description
Calculates graph assortativity
Usage
assort(G, mode = "in.out")
Arguments
G |
Graph object of class |
mode |
One of |
Details
The definitive measure of graph assortativity is the Pearson correlation coefficient of the degree of pairs of adjacent nodes (Newman, 2002). Let \overrightarrow{u_iv_i}
define nodes and directionality of the ith arc, i=1,2,3,\ldots,m
, let \gamma,\tau\in{-,+}
index the degree type: -=in, +=out
, and let \left(u_i^\gamma,v_i^\tau\right)
, be the \gamma-
and \tau-
degree of the ith arc. Then, the general form of assortativity index is:
r\left(\gamma,\tau\right)=m^{-1}\frac{\sum_{i= 1}^m (u_i^\gamma-\bar{u}^\gamma)(v^\tau_i-\bar{v}^\tau)}{s^\gamma s^\tau}
where \bar{u}^\gamma
and \bar{v}^\gamma
are the arithmetic means of the u_i^\gamma
s and v_i^\tau
s, and s^\gamma
and s^\tau
are the population standard deviations of the u_i^\gamma
s and v_i^\tau
s. Under this framework, there are four possible forms to r\left(\gamma,\tau\right)
(Foster et al., 2010). These are: r\left(+,-\right), r\left(-,+\right), r\left(-,-\right)
, and r\left(+,+\right)
.
Value
Assortativity coefficeint outcome(s)
Author(s)
Ken Aho, Gabor Csardi wrote degree
References
Newman, M. E. (2002). Assortative mixing in networks. Physical Review Letters, 89(20), 208701.
Foster, J. G., Foster, D. V., Grassberger, P., & Paczuski, M. (2010). Edge direction and the structure of networks. Proceedings of the National Academy of Sciences, 107(24), 10815-10820.
Examples
network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, e --+ j,
j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, l --+ m, m --+ n,
n --+ o)
assort(network_a)