  Complex networks are often constructed by aggregating empirical data over
time, such that a link represents the existence of interactions between the
endpoint nodes and the link weight represents the intensity of such
interactions within the aggregation time window. The resulting networks are
then often considered static. More often than not, the aggregation time window
is dictated by the availability of data, and the effects of its length on the
resulting networks are rarely considered. Here, we address this question by
studying the structural features of networks emerging from aggregating
empirical data over different time intervals, focussing on networks derived
from time-stamped, anonymized mobile telephone call records. Our results show
that short aggregation intervals yield networks where strong links associated
with dense clusters dominate; the seeds of such clusters or communities become
already visible for intervals of around one week. The degree and weight
distributions are seen to become stationary around a few days and a few weeks,
respectively. An aggregation interval of around 30 days results in the stablest
similar networks when consecutive windows are compared. For longer intervals,
the effects of weak or random links become increasingly stronger, and the
average degree of the network keeps growing even for intervals up to 180 days.
The placement of the time window is also seen to affect the outcome: for short
windows, different behavioural patterns play a role during weekends and
weekdays, and for longer windows it is seen that networks aggregated during
holiday periods are significantly different.

Physics and Society;Social and Information Networks