  With the growing amount of available temporal real-world network data, an
important question is how to efficiently study these data. One can simply model
a temporal network as either a single aggregate static network, or as a series
of time-specific snapshots, each of which is an aggregate static network over
the corresponding time window. The advantage of modeling the temporal data in
these two ways is that one can use existing well established methods for static
network analysis to study the resulting aggregate network(s). Here, we develop
a novel approach for studying temporal network data more explicitly. We base
our methodology on the well established notion of graphlets (subgraphs), which
have been successfully used in numerous contexts in static network research.
Here, we take the notion of static graphlets to the next level and develop new
theory needed to allow for graphlet-based analysis of temporal networks. Our
new notion of dynamic graphlets is quite different than existing approaches for
dynamic network analysis that are based on temporal motifs (statistically
significant subgraphs). Namely, these approaches suffer from many limitations.
For example, they can only deal with subgraph structures of limited complexity.
Also, their major drawback is that their results heavily depend on the choice
of a null network model that is required to evaluate the significance of a
subgraph. However, choosing an appropriate null network model is a non-trivial
task. Our dynamic graphlet approach overcomes the limitations of the existing
temporal motif-based approaches. At the same time, when we thoroughly evaluate
the ability of our new approach to characterize the structure and function of
an entire temporal network or of individual nodes, we find that the dynamic
graphlet approach outperforms the static graphlet approach, which indicates
that accounting for temporal information helps.
