assortativity(graph, types1, types2 = NULL, directed = TRUE)assortativity_nominal(graph, types, directed = TRUE)
assortativity_degree(graph, directed = TRUE)
NULL here if
you want to use the same values for outgoing and incoming edges. This
argument is ignored (with a warning) if iTRUE here to do the natural thing, i.e. use directed version of the
measure for directed graphs and the undirectedas.integer.M.E.J. Newman defined two kinds of assortativity coefficients, the first one
is for categorical labels of vertices. assortativity_nominal
calculates this measure. It is defines as
$$r=\frac{\sum_i e_{ii}-\sum_i a_i b_i}{1-\sum_i a_i b_i}$$
where $e_{ij}$ is the fraction of edges connecting vertices of type $i$ and $j$, $a_i=\sum_j e_{ij}$ and $b_j=\sum_i e_{ij}$.
The second assortativity variant is based on values assigned to the
vertices. assortativity calculates this measure. It is defined as
$$r=\frac1{\sigma_q^2}\sum_{jk} jk(e_{jk}-q_j q_k)$$
for undirected graphs ($q_i=\sum_j e_{ij}$) and as
$$r=\frac1{\sigma_o\sigma_i}\sum_{jk}jk(e_{jk}-q_j^o q_k^i)$$
for directed ones. Here $q_i^o=\sum_j e_{ij}$, $q_i^i=\sum_j e_{ji}$, moreover, $\sigma_q$, $sigma_o$ and $sigma_i$ are the standard deviations of $q$, $q^o$ and $q^i$, respectively.
The reason of the difference is that in directed networks the relationship is not symmetric, so it is possible to assign different values to the outgoing and the incoming end of the edges.
assortativity_degree uses vertex degree (minus one) as vertex values
and calls assortativity.
M. E. J. Newman: Assortative mixing in networks, Phys. Rev. Lett. 89,
208701 (2002)
# random network, close to zero
assortativity_degree(sample_gnp(10000, 3/10000))
# BA model, tends to be dissortative
assortativity_degree(sample_pa(10000, m=4))Run the code above in your browser using DataLab