A tidy description of the whole network, one row per property. Two densities are reported and they answer different questions. Snapshot density is the mean over time bins of realised against possible edges. Temporal density is the proportion of all possible relational exposure occupied during the observation window. Overlapping and duplicate spells for the same ordered pair, or dyad in an undirected network, are unioned before their duration is counted.
Usage
# S3 method for class 'dynet'
summary(object, temporal_density = FALSE, ...)Arguments
- object
A temporal network from
dynet().- temporal_density
Whether to compute the temporal-density row.
FALSE, the default, reports"not computed"for it. The quantity integrates exact occupancy over every eligible ordered pair, so its cost grows with the square of the vertex count: on a 442-vertex forum network it takes about 32 seconds, while every other row in the table is immediate. PassTRUEwhen the number is wanted.- ...
Ignored.
Details
Let \(Y_q(t)\) indicate that both endpoints of relational opportunity
\(q\) are eligible at positive observed time \(t\), and let
\(E_q(t)\) indicate binary union edge activity. Temporal density is
$$\rho = \frac{\sum_q \int Y_q(t)E_q(t)dt}
{\sum_q \int Y_q(t)dt}.$$
Directed opportunities are ordered; undirected opportunities are unordered.
The integrals are evaluated exactly over observation, vertex, and edge change
points. Self-loops, weights, session labels, duplicate spells, genuine
points, and observation gaps do not add exposure. A network with no positive
time containing two coeligible distinct vertices has undefined temporal
density and reports NA.
This is an occupancy definition. Unlike summing spell durations, it remains
in [0, 1] when the same relation has overlapping or duplicated spells.
References
Bender-deMoll, S., & Morris, M. (2025). tsna: Tools for Temporal Social Network Analysis. R package version 0.3.6.
Holme, P., & Saramaki, J. (2012). Temporal networks. Physics Reports, 519(3), 97-125.
Latapy, M., Viard, T., & Magnien, C. (2018). Stream graphs and link streams for the modeling of interactions over time. Social Network Analysis and Mining, 8, 61.
Examples
dn <- dynet(school_contacts)
summary(dn)
#> property value
#> 1 format interval
#> 2 directed yes
#> 3 vertices 14
#> 4 edge spells 240
#> 5 distinct pairs 110
#> 6 time unit step
#> 7 observed from 0
#> 8 observed to 21.52
#> 9 span 21.52
#> 10 bin width 1
#> 11 time bins 22
#> 12 mean snapshot density 0.0829
#> 13 temporal density not computed
#> 14 sessions none
#> 15 vertex attributes none
# The temporal density is opt-in, since it is quadratic in the vertex count.
summary(dn, temporal_density = TRUE)
#> property value
#> 1 format interval
#> 2 directed yes
#> 3 vertices 14
#> 4 edge spells 240
#> 5 distinct pairs 110
#> 6 time unit step
#> 7 observed from 0
#> 8 observed to 21.52
#> 9 span 21.52
#> 10 bin width 1
#> 11 time bins 22
#> 12 mean snapshot density 0.0829
#> 13 temporal density 0.0285
#> 14 sessions none
#> 15 vertex attributes none