assort: Assortativity

In streamDAG: Analytical Methods for Stream DAGs

Assortativity

Description

Calculates graph assortativity

Usage

assort(G, mode = "in.out")

Arguments

G	Graph object of class igraph. See graph_from_literal.
mode	One of "in.in", "in.out", "out.out", "out.in", or "all".

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^\gammas and v_i^\taus, and s^\gamma and s^\tau are the population standard deviations of the u_i^\gammas and v_i^\taus. 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)

streamDAG documentation built on Oct. 7, 2023, 1:08 a.m.