computes graph-level statistics for netify objects, including density, reciprocity, centralization measures, and custom metrics. handles cross-sectional and longitudinal networks, as well as multilayer structures.
Usage
# S3 method for class 'netify'
summary(object, ...)Value
a data frame with one row per network/time period containing:
basic network properties:
netnetwork/time identifier
layerlayer name (for multilayer networks)
num_actorsnumber of actors (or
num_row_actorsandnum_col_actorsfor bipartite networks)densityproportion of possible ties that exist
num_edgestotal number of edges (count of every non-zero entry; for signed networks, negative-weight ties are included alongside positive ones)
prop_edges_missingproportion of potential edge dyads that are na. uses the same denominator as
density(off-diagonal cells for unipartite withdiag_to_NA, halved for symmetric networks, all cells for bipartite), sodensity + prop_edges_missing + observed_zero_fraction = 1.prop_unknown_edgesproportion of potential edges that are na because they were unobserved at the data-entry stage (as opposed to structurally absent or on-diagonal). only appears when the netlet was built with
missing_to_zero = FALSE; otherwise unobserved dyads have been filled with 0 and the column would be identically zero.
for weighted networks only:
mean_edge_weightaverage weight of realized non-zero edges. signed networks include negative ties; observed zero non-ties and missing dyads are excluded.
sd_edge_weightstandard deviation of realized non-zero edge weights
median_edge_weightmedian realized non-zero edge weight
min_edge_weight,max_edge_weightrange of realized non-zero edge weights
structural measures:
competition(orcompetition_row/competition_col)herfindahl-hirschman index measuring concentration of ties. calculated as \(\sum_{i=1}^{n} (s_i)^2\) where \(s_i\) is actor i's share of total ties. ranges from 1/n (equal distribution) to 1 (one actor has all ties).
sd_of_actor_means(orsd_of_row_means/sd_of_col_means)standard deviation of actors' average tie strengths, measuring heterogeneity in actor activity levels
transitivityglobal clustering coefficient (probability that two neighbors of a node are connected). returns
nawhen the coefficient is undefined.
for directed networks only:
covar_of_row_col_meanscorrelation between actors' sending and receiving means. the column name is retained for compatibility.
reciprocitypearson correlation between the adjacency matrix and its transpose. this measures the linear association between outgoing and incoming tie weights for each dyad (i.e., how similar \(a_{ij}\) is to \(a_{ji}\) across all dyads). values near 1 indicate strong reciprocity, while values near 0 indicate no relationship. note: this differs from the traditional edge-based reciprocity (proportion of mutual dyads) used by igraph and other packages.
mutualproportion of mutual dyads: the fraction of connected dyad pairs where both directions are present. ranges from 0 (no mutual ties) to 1 (all ties are reciprocated). this is the traditional edge-based reciprocity measure used by igraph and most network analysis textbooks.
Details
the function automatically adapts calculations based on network properties:
bipartite networks: reports row and column actors separately
directed networks: calculates separate statistics for in/out ties
weighted networks: includes weight-based statistics
multilayer networks: processes each layer independently
longitudinal networks: calculates statistics for each time period
competition index interpretation:
the competition measure (hhi) captures how concentrated network ties are among actors. low values indicate distributed activity across many actors (competitive), while high values indicate concentration among few actors (monopolistic). this is particularly useful for analyzing power dynamics or resource distribution in networks.
custom statistics:
add custom graph-level metrics using the other_stats parameter:
# example: community detection
modularity_stat <- function(net) {
g <- netify_to_igraph(net)
comm <- igraph::cluster_walktrap(g)
c(modularity = igraph::modularity(comm),
n_communities = length(unique(comm$membership)))
}
summary(net, other_stats = list(community = modularity_stat))Note
for large longitudinal or multilayer networks, computation can be intensive.
consider using subset_netify to analyze specific time periods
or layers.
density uses the full potential-dyad denominator. missing edges (na values)
are not counted as present ties; they are reported separately in
prop_edges_missing.
References
dorff, c., gallop, m., & minhas, s. (2023). "networks of violence: predicting conflict in nigeria." journal of politics, 85(1).
Examples
# load example data
data(icews)
# \donttest{
# basic usage
net <- netify(
icews,
actor1 = "i", actor2 = "j", time = "year",
symmetric = FALSE,
weight = "verbCoop"
)
# get summary
summary(net)
#> net num_actors density num_edges prop_edges_missing mean_edge_weight
#> 1 2002 152 0.3787034 8692 0 51.73240
#> 2 2003 152 0.3871994 8887 0 50.00934
#> 3 2004 152 0.4145173 9514 0 47.88669
#> 4 2005 152 0.4071976 9346 0 48.61245
#> 5 2006 152 0.4108139 9429 0 51.34044
#> 6 2007 152 0.4243203 9739 0 51.60612
#> 7 2008 152 0.4351690 9988 0 48.33480
#> 8 2009 152 0.4293308 9854 0 47.35600
#> 9 2010 152 0.4346462 9976 0 41.72113
#> 10 2011 152 0.4229697 9708 0 37.33642
#> 11 2012 152 0.4287644 9841 0 37.30637
#> 12 2013 152 0.4318142 9911 0 39.86207
#> 13 2014 152 0.4258452 9774 0 43.19153
#> sd_edge_weight median_edge_weight min_edge_weight max_edge_weight
#> 1 230.1314 8 1 6003
#> 2 229.0646 7 1 5937
#> 3 210.7666 7 1 5141
#> 4 229.9569 6 1 6561
#> 5 246.6313 7 1 7579
#> 6 246.2486 7 1 7125
#> 7 221.5845 7 1 6091
#> 8 236.4214 6 1 6889
#> 9 198.3157 6 1 4937
#> 10 172.2944 5 1 5581
#> 11 161.8837 6 1 4225
#> 12 196.2998 5 1 6320
#> 13 206.6673 6 1 6327
#> competition_row competition_col sd_of_row_means sd_of_col_means
#> 1 0.04093116 0.03813621 44.91530 43.04935
#> 2 0.04199822 0.03930188 45.07759 43.32783
#> 3 0.03481011 0.03262993 41.25503 39.63005
#> 4 0.04067046 0.03624472 45.20964 42.17312
#> 5 0.04151400 0.03697499 48.76301 45.48502
#> 6 0.03887627 0.03514325 48.67808 45.77854
#> 7 0.03785375 0.03421258 46.01192 43.25059
#> 8 0.04500583 0.03915054 49.29918 45.38806
#> 9 0.04071163 0.03493156 41.44120 37.76971
#> 10 0.03964994 0.03405077 35.52390 32.37731
#> 11 0.03587638 0.03146233 33.86660 31.21128
#> 12 0.04058869 0.03642385 39.26572 36.78299
#> 13 0.04058415 0.03521224 41.95447 38.49827
#> covar_of_row_col_means reciprocity mutual transitivity
#> 1 0.9946888 0.9778217 0.8537001 0.6058952
#> 2 0.9872959 0.9632488 0.8479933 0.6072045
#> 3 0.9923809 0.9769563 0.8452289 0.6215978
#> 4 0.9932157 0.9804325 0.8386779 0.6215075
#> 5 0.9909337 0.9771928 0.8510012 0.6277829
#> 6 0.9940837 0.9783703 0.8511690 0.6330626
#> 7 0.9916659 0.9694667 0.8468935 0.6401296
#> 8 0.9946612 0.9800665 0.8467016 0.6318319
#> 9 0.9934913 0.9823385 0.8402509 0.6386063
#> 10 0.9903188 0.9763723 0.8327355 0.6220630
#> 11 0.9877987 0.9702754 0.8336128 0.6337725
#> 12 0.9939394 0.9782226 0.8248941 0.6314429
#> 13 0.9904402 0.9730745 0.8389464 0.6297063
# }
if (FALSE) { # \dontrun{
# add custom statistics - community detection
comm_stats <- function(mat) {
g <- netify_to_igraph(mat)
comm <- igraph::cluster_spinglass(g)
c(
n_communities = length(comm$csize),
modularity = comm$modularity
)
}
# apply to subset for efficiency
sub_net <- subset_netify(net, time = as.character(2013:2014))
summary(sub_net, other_stats = list(community = comm_stats))
} # }