assort function

Assortativity

Calculates graph assortativity

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:

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 $r\left(+,+\right)$.

Returns

Assortativity coefficeint outcome(s)

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.

Author(s)

Ken Aho, Gabor Csardi wrote degree

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)