[igraph] Assortativity value NaN for regular networks

[Borja Esteve-Altava]

Hi everyone,

I want to use the assortativity degree as a ways of estimating the level of
homogeneity / heterogeneity of real networks:
1 = homogeneous (all vertices having degree k, they all connect to vertices
with degree k)
-1 = heterogeneous

assortativity_degree(make_star(25, mode = "undirected"), directed=FALSE)

[1] -1

However, for the other extreme of homogeneity (e.g., regular networks) the
function assortativity_degree() does not return a value of 1, but a NaN.

assortativity_degree(make_lattice(c(1, 5, 5), circular=T), directed=FALSE)

[1] NaN

When I tried to do an "almost-regular" network by deleting one edge in the
regular, instead of getting a close to 1 value I got a close to 0 value.

assortativity_degree(make_lattice(c(1, 5, 5), circular = T) %>%

delete_edges(1), directed=F)
[1] -0.06521739

Any clue why regular networks do not show values of 1?
Am I missing something about how assortativity is calculated?

Thanks a lot!

[Szabolcs Horvát]

Hello Borja,

If you go back to the mathematical definition of assortativity, it makes
perfect sense. It is a normalized correlation. If all degrees are the
same, then the correlation is 0, and so is the variance, 0/0 -> NaN. If
the degrees are *almost* the same, then the correlation is almost zero, the
variance is nonzero, verysmall / nonzero -> verysmall.

Intuitively, your regular network is not special among networks with the
same degrees: the vertices have no choice but to connect to other vertices
of the same degree. Compare with networks with a wide range of degrees
present: some of these are assortative, some aren't. Unlike in the case of
regular graphs, there's a freedom.

Post by Borja Esteve-Altava
Hi everyone,
I want to use the assortativity degree as a ways of estimating the level
1 = homogeneous (all vertices having degree k, they all connect to
vertices with degree k)
-1 = heterogeneous

assortativity_degree(make_star(25, mode = "undirected"), directed=FALSE)

[1] -1
However, for the other extreme of homogeneity (e.g., regular networks) the
function assortativity_degree() does not return a value of 1, but a NaN.

assortativity_degree(make_lattice(c(1, 5, 5), circular=T),

directed=FALSE)
[1] NaN
When I tried to do an "almost-regular" network by deleting one edge in the
regular, instead of getting a close to 1 value I got a close to 0 value.

assortativity_degree(make_lattice(c(1, 5, 5), circular = T) %>%

delete_edges(1), directed=F)
[1] -0.06521739
Any clue why regular networks do not show values of 1?
Am I missing something about how assortativity is calculated?
Thanks a lot!
--
*Borja*
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