Calculate EI-Index of ego networks

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-/heterophily - use comp_ei(). for that variant of the EI-Index.

Usage

EI(object, alt.attr, include.ego = FALSE, ego.attr = alt.attr, rescale = TRUE)

Arguments

object: An egor object.
alt.attr: Character naming grouping variable.
include.ego: Logical. Include or exclude ego from EI calculation.
ego.attr: Character, naming the ego variable corresponding to ego.attr. Defaults to ego.attr.
rescale: Logical. If TRUE, the EI index calculation is re-scaled, so that the EI is not distorted by differing group sizes.

Value

Returns tibble with the following columns:

ego ID (".egoID")
network EI-Index ("ei")
subgroup EI-Index values (named by value levels of alt.attr/ego.attr)

Details

The 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. The re-scaled 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.

References

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.

Examples

data("egor32")
EI(egor32, "sex")
#> # A tibble: 32 × 4
#>    .egoID       ei        m        w
#>     <dbl>    <dbl>    <dbl>    <dbl>
#>  1      1 -0.123   -0.167   -0.100  
#>  2      2 -0.0608  -0.0323  -0.0667 
#>  3      3 -0.122   -0.190    0.448  
#>  4      4 -0.231   -0.0323  -0.263  
#>  5      5  0.0448  -0.0141   0.111  
#>  6      6  0.141   -0.00917  0.674  
#>  7      7  0.00705 -0.119    0.0389 
#>  8      8 -0.123    0.0588  -0.355  
#>  9      9 -0.0606  -0.181    0.00990
#> 10     10 -0.0286  -0.25     0.0370 
#> # ℹ 22 more rows