  In this paper, we investigate the phenomenon of "age-specific small worlds"
using data from a large-scale mobile communication network approximating
interaction patterns at societal scale. Rather than asking whether two random
individuals are separated by a small number of links, we ask whether
individuals in specific age groups live in a small world in relation to
individuals from other age groups. Our analysis shows that there is systematic
variation in this age-relative small world effect. Young people live in the
"smallest world," being separated from other young people and their parent's
generation via a smaller number of intermediaries than older individuals. The
oldest people live in the "least small world," being separated from their same
age peers and their younger counterparts by a larger number of intermediaries.
Variation in the small world effect is specific to age as a node attribute
(being absent in the case of gender) and is consistently observed under several
data robustness checks. The discovery of age-specific small worlds is
consistent with well-known social mechanisms affecting the way age interacts
with network connectivity and the relative prevalence of kin ties and non-kin
ties observed in this network. This social pattern has significant implications
for our understanding of generation-specific dynamics of information cascades,
diffusion phenomena, and the spread of fads and fashions.
