The EI-Index is the division of the surplus count intra-group edges over inter-group edges,
divided by total count of all edges.
This implementation uses the intra-group and inter-group density instead
of edge counts, when
rescale is set to
TRUE (default). The EI-Index is calculated for
the whole network and for subgroups. Alternatively, the EI index can be employed as a measurement
for egos tendency to homo-/heteorphily - use
for that variant of the EI-Index.
EI(object, alt.attr, include.ego = FALSE, ego.attr = alt.attr, rescale = TRUE)
tibble with the following columns:
ego ID (".egoID")
network EI-Index ("ei")
subgroup EI-Index values (named by value levels of
whole network EI is a metric indicating the tendency of a network to be
clustered by the categories of a given factor variable (
alt.attr). The EI value of a
group describes the tendency of that group within a network to be connected
(if between 0 and 1) or not connected (if between -1 and 0)
to other groups. Differing group sizes can lead to a distortion of EI values
i.e. the ability of a big group A to form relationships to much smaller group B
is limited by the size of B. Even when all possible edges between A and B exist,
the EI value for group A might still be negative, classifying it as homophile.
rescaled EI-Index values provided by this implementation substitutes absolute
edge counts by inter- and intra-group edge densities in order to avoid the
distortion of the EI-Index values. These values express the extend of homo- or heterophily
of the network and its subgroups, as made possible by subgroup sizes.
Krackhardt, D., Stern, R.N., 1988. Informal networks and organizational crises: an experimental simulation. Social Psychology Quarterly 51 (2), 123-140.
Everett, M. G., & Borgatti, S. P. (2012). Categorical attribute based centrality: E-I and G-F centrality. Social Networks, 34(4), 562-569.
comp_ei(), for an ego level homophily measure.
data("egor32") EI(egor32, "sex")#> # A tibble: 32 x 4 #> .egoID ei m w #> <fct> <dbl> <dbl> <dbl> #> 1 1 0.28 0.250 1 #> 2 2 0.0537 0.0430 0.0886 #> 3 3 -0.110 -0.0849 -0.151 #> 4 4 0.0198 0.125 -0.150 #> 5 5 0.0191 0 0.176 #> 6 6 -0.160 -0.101 -0.245 #> 7 7 0.0931 0.0588 0.233 #> 8 8 0.0820 0.111 0.0244 #> 9 9 0.158 0.2 -0.333 #> 10 10 -0.0581 0.0588 -0.321 #> # … with 22 more rows