The input graph, it can be directed or undirected.
types1
The vertex values, these can be arbitrary numeric values.
types2
A second value vector to be using for the incoming edges when
calculating assortativity for a directed graph. Supply NULL here if
you want to use the same values for outgoing and incoming edges. This
argument is ignored (with a warning) if it is not NULL and undirected
assortativity coefficient is being calculated.
directed
Logical scalar, whether to consider edge directions for
directed graphs. This argument is ignored for undirected graphs. Supply
TRUE here to do the natural thing, i.e. use directed version of the
measure for directed graphs and the undirected version for undirected
graphs.
types
Vector giving the vertex types. They as assumed to be integer
numbers, starting with one. Non-integer values are converted to integers
with as.integer.
Details
The assortativity coefficient measures the level of homophyly of the graph,
based on some vertex labeling or values assigned to vertices. If the
coefficient is high, that means that connected vertices tend to have the
same labels or similar assigned values.
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
for directed ones. Here qout(i)=sum(e(i,j), j),
qin(i)=sum(e(j,i), j), moreover,
sigma(q), sigma(qout) and
sigma(qin) are the standard deviations of q,
qout and qin, 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.
# 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))