Summary method to get actor level statistics for netify objects
summary_actor.Rdsummary_actor provides detailed actor-level statistics for netify objects, handling different network structures and weight conditions. It produces a data frame summarizing various network metrics like degree, strength, closeness, betweenness, and centrality measures.
Arguments
- netlet
Object of class
netify, typically produced byget_adjacencyor other network creation functions within the package.- invert_weights_for_igraph
Logical; if TRUE, the weights of the edges are inverted before being used in the calculation of closeness or betweenness centrality. This is because igraph treats edge weights as distances. Inverting weights can be crucial when higher weights should imply stronger (or more valuable) connections rather than longer distances. Default is TRUE.
- other_stats
A named list of functions that take a matrix and return additional actor-level statistics to be included in the output. Each function should accept a matrix as input and return a vector or single value per actor. This allows for the inclusion of custom metrics in the summary output.
Value
A data.frame object summarizing actor-level statistics of the network(s). Depending on the structure and attributes of the netify object, the output includes:
Symmetric Unweighted: Various network measures for actor \(i\) include:
Degree: The count of unique actors that actor \(i\) is directly connected to – calculated as \(d_i = \sum_{j=1}^{n} a_{ij}\), where \(a_{ij}\) is the adjacency matrix element indicating the presence (1) or absence (0) of a tie between actors \(i\) and \(j\).
Proportion of ties: The percentage of actors in the network with whom actor \(i\) has a direct relationship – calculated as \(p_i = \frac{d_i}{n-1}\), where \(d_i\) is the degree of actor \(i\) and \(n\) is the total number of actors in the network.
Network share: The fraction of the network's total connections that include actor \(i\) – calculated as \(s_i = \frac{d_i}{\sum_{j=1}^{n} d_j}\), where \(d_i\) is the degree of actor \(i\) and \(\sum_{j=1}^{n} d_j\) is the total number of ties in the network.
Closeness (\(C_i\)): A measure of how close actor \(i\) is to all other actors in the network – calculated as \(C_i = \frac{1}{\sum_{j} d(i, j)}\), where \(d(i, j)\) is the distance to every other actor \(j\).
Betweenness (\(B_i\)): A measure of actor \(i\)'s importance in connecting different parts of the network – calculated as \(B_i = \sum_{s \neq i \neq t} \frac{\sigma_{st}(i)}{\sigma_{st}}\), where \(\sigma_{st}\) is the total number of shortest paths from node \(s\) to node \(t\) and \(\sigma_{st}(i)\) is the number of those paths that pass through \(i\).
Eigenvector centrality (\(EC_i\)): A measure of actor \(i\)'s influence based on their connections to other highly connected actors in the network, calculated using the principal eigenvector of the network's adjacency matrix.
Symmetric Weighted: Includes the same statistics as the symmetric unweighted case, with additional measures accounting for the weight of connections:
Strength sum: The total weight of the ties connected to actor \(i\) in the network – calculated as \(s_i^{sum} = \sum_{j=1}^{n} w_{ij}\), where \(w_{ij}\) is the weight of the tie between actors \(i\) and \(j\).
Strength average: The average weight of the ties connected to actor \(i\) – calculated as \(s_i^{avg} = \frac{s_i^{sum}}{d_i}\), where \(s_i^{sum}\) is the strength sum of actor \(i\) and \(d_i\) is the degree of actor \(i\).
Strength standard deviation: The variability in the weights of ties connected to actor \(i\) – calculated as \(s_i^{sd} = \sqrt{\frac{1}{d_i} \sum_{j=1}^{n} (w_{ij} - s_i^{avg})^2}\), where \(w_{ij}\) is the weight of the tie between actors \(i\) and \(j\).
Strength median: The median weight of the ties connected to actor \(i\) – calculated as the middle value of the sorted weights.
For closeness and betweenness, edge weights are typically inverted to treat them as distances, following the convention in
igraph. This behavior can be modified by setting theinvert_weights_for_igraphparameter in thesummary_actorfunction to FALSE.Asymmetric Unweighted: Same as the symmetric case but now a statistics for the row and column are calculated separately; when relevant a total statistic is calculated as well.
Asymmetric Weighted: Same as the symmetric case but now a statistics for the row and column are calculated separately; when relevant a total statistic is calculated as well.
Details
The function automatically adjusts calculations based on network symmetry and weight attributes, offering tailored statistical outputs for comprehensive network analysis. It supports handling of both cross-sectional and longitudinal network data, ensuring that each actor's metrics are accurately computed over time if applicable. Examples of additional computations (like authority or hub scores) are provided only for asymmetric networks.
Examples
# load icews data
data(icews)
# create a netify object
netlet = netify(
dyad_data=icews, actor1='i', actor2='j',
time = 'year',
symmetric=FALSE, weight='verbCoop',
mode='unipartite', sum_dyads=FALSE,
actor_time_uniform=TRUE, actor_pds=NULL,
diag_to_NA=TRUE, missing_to_zero=TRUE
)
# get actor-level statistics
actor_stats <- summary_actor(netlet)
head(actor_stats)
#> actor time degree_in degree_out degree_total prop_ties_in prop_ties_out
#> 1 Afghanistan 2002 81 92 173 0.5364238 0.6092715
#> 2 Albania 2002 49 46 95 0.3245033 0.3046358
#> 3 Algeria 2002 65 68 133 0.4304636 0.4503311
#> 4 Angola 2002 67 64 131 0.4437086 0.4238411
#> 5 Argentina 2002 48 48 96 0.3178808 0.3178808
#> 6 Armenia 2002 66 71 137 0.4370861 0.4701987
#> prop_ties_total strength_sum_in strength_sum_out strength_sum_total
#> 1 1 8694 10160 18854
#> 2 1 943 1022 1965
#> 3 1 1123 1205 2328
#> 4 1 1111 1311 2422
#> 5 1 1261 1427 2688
#> 6 1 2642 2665 5307
#> strength_avg_in strength_avg_out strength_avg_total strength_std_in
#> 1 57.576159 67.284768 62.430464 198.98323
#> 2 6.245033 6.768212 6.506623 21.17104
#> 3 7.437086 7.980132 7.708609 17.00179
#> 4 7.357616 8.682119 8.019868 20.18988
#> 5 8.350993 9.450331 8.900662 39.54933
#> 6 17.496689 17.649007 17.572848 62.13790
#> strength_std_out strength_std_total strength_median_in strength_median_out
#> 1 227.24232 213.11277 1 2
#> 2 22.27089 21.72096 0 0
#> 3 18.93197 17.96688 0 0
#> 4 24.29633 22.24310 0 0
#> 5 45.34294 42.44614 0 0
#> 6 66.88569 64.51180 0 0
#> strength_median_total network_share_in network_share_out network_share_total
#> 1 1.5 0.019334694 0.022594950 0.020964822
#> 2 0.0 0.002097149 0.002272838 0.002184994
#> 3 0.0 0.002497454 0.002679814 0.002588634
#> 4 0.0 0.002470767 0.002915549 0.002693158
#> 5 0.0 0.002804354 0.003173523 0.002988938
#> 6 0.0 0.005875577 0.005926727 0.005901152
#> closeness_in closeness_out closeness_all betweenness authority_score
#> 1 71.13409 68.44904 78.06787 1.324503e-02 0.26866096
#> 2 42.48817 43.64733 47.16201 0.000000e+00 0.01252200
#> 3 44.78256 39.95772 47.41426 0.000000e+00 0.01406673
#> 4 51.35489 46.60123 54.85391 8.830022e-05 0.01905067
#> 5 63.91481 61.26657 69.47750 0.000000e+00 0.03580770
#> 6 65.51012 63.04273 71.46157 0.000000e+00 0.05049222
#> hub_score
#> 1 0.183233794
#> 2 0.009730031
#> 3 0.010671854
#> 4 0.011275109
#> 5 0.024732267
#> 6 0.039622725
# add statistic that get
# the max incoming and outgoing tie
max_out <- function(mat){ apply(mat, 1, max, na.rm=TRUE) }
max_in <- function(mat){ apply(mat, 2, max, na.rm=TRUE) }
actor_stats_custom <- summary_actor(netlet, other_stats = list(max_out = max_out, max_in = max_in))
head(actor_stats_custom)
#> actor time degree_in degree_out degree_total prop_ties_in prop_ties_out
#> 1 Afghanistan 2002 81 92 173 0.5364238 0.6092715
#> 2 Albania 2002 49 46 95 0.3245033 0.3046358
#> 3 Algeria 2002 65 68 133 0.4304636 0.4503311
#> 4 Angola 2002 67 64 131 0.4437086 0.4238411
#> 5 Argentina 2002 48 48 96 0.3178808 0.3178808
#> 6 Armenia 2002 66 71 137 0.4370861 0.4701987
#> prop_ties_total strength_sum_in strength_sum_out strength_sum_total
#> 1 1 8694 10160 18854
#> 2 1 943 1022 1965
#> 3 1 1123 1205 2328
#> 4 1 1111 1311 2422
#> 5 1 1261 1427 2688
#> 6 1 2642 2665 5307
#> strength_avg_in strength_avg_out strength_avg_total strength_std_in
#> 1 57.576159 67.284768 62.430464 198.98323
#> 2 6.245033 6.768212 6.506623 21.17104
#> 3 7.437086 7.980132 7.708609 17.00179
#> 4 7.357616 8.682119 8.019868 20.18988
#> 5 8.350993 9.450331 8.900662 39.54933
#> 6 17.496689 17.649007 17.572848 62.13790
#> strength_std_out strength_std_total strength_median_in strength_median_out
#> 1 227.24232 213.11277 1 2
#> 2 22.27089 21.72096 0 0
#> 3 18.93197 17.96688 0 0
#> 4 24.29633 22.24310 0 0
#> 5 45.34294 42.44614 0 0
#> 6 66.88569 64.51180 0 0
#> strength_median_total network_share_in network_share_out network_share_total
#> 1 1.5 0.019334694 0.022594950 0.020964822
#> 2 0.0 0.002097149 0.002272838 0.002184994
#> 3 0.0 0.002497454 0.002679814 0.002588634
#> 4 0.0 0.002470767 0.002915549 0.002693158
#> 5 0.0 0.002804354 0.003173523 0.002988938
#> 6 0.0 0.005875577 0.005926727 0.005901152
#> closeness_in closeness_out closeness_all betweenness authority_score
#> 1 71.13409 68.44904 78.06787 1.324503e-02 0.26866096
#> 2 42.48817 43.64733 47.16201 0.000000e+00 0.01252200
#> 3 44.78256 39.95772 47.41426 0.000000e+00 0.01406673
#> 4 51.35489 46.60123 54.85391 8.830022e-05 0.01905067
#> 5 63.91481 61.26657 69.47750 0.000000e+00 0.03580770
#> 6 65.51012 63.04273 71.46157 0.000000e+00 0.05049222
#> hub_score max_out max_in
#> 1 0.183233794 1516 1847
#> 2 0.009730031 160 157
#> 3 0.010671854 91 114
#> 4 0.011275109 147 176
#> 5 0.024732267 424 469
#> 6 0.039622725 547 609