Information Technology Reference
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Fig. 1.
The importance of the sampling window length
to the length of the cumulation time window and its effect to the aggregated
network's properties.
In the following, the term
snapshot network
will refer to a network at time
t
:
G
t
(
V
t
,E
t
). The aggregated network from
t
0
to
t
,
G
t
=(
E
i
) will be
called a
cumulative network
. Clearly, snapshot networks and their aggregations
with various lengths could be very different. See Figure 1 as an illustration.
In our previous works (see [1], [2], [3], [5] and [4] as an extensive summary) we
evaluated the properties of various elementary dynamic network models. In this
paper, we extend these studies by comparing the results of artifical simulations
to a selected set of empirical data available in the social science literature. Our
goal is to validate the previous theoretical results against data obtained from a
real-world system.
The paper is structured as follows. The next section briefly discusses our pre-
vious results and conclusions regarding the elementary dynamic network models.
Section 3 describes the chosen empirical datasets and reports our results, while
the last section outlines the directions for future work and concludes the paper.
∪
i
=
t
0
V
i
,
∪
i
=
t
0
2 Dynamic Network Models
Constructing a static network for further analysis in general requires either a
snapshot of a network in a specific point of time, or some kind of aggregation
(e.g. collecting longitudinal samples of networks). However, both approaches may
miss important facts and tendencies of network dynamics: the ongoing change
of a network may be among the most interesting properties to observe. For
instance, dissemination of information, social norms, innovation, or even diseases
may behave in an inherently different way if we use different time windows for
our investigation (e.g. the dynamic interpretation lets us observe individuals
switching aliations periodically in community identification [16]).
In our previous studies [4] we defined elementary models of dynamic networks
based on the classic network models for static networks. We also analyzed models
[3] where edges appear periodically in each
k
∗
t
time step: random links are
