  The cover time of random walks on a graph has found wide practical
applications in different fields of computer science, such as crawling and
searching on the World Wide Web and query processing in sensor networks, with
the application effects dependent on the behavior of cover time: the smaller
the cover time, the better the application performance. It was proved that over
all graphs with $N$ nodes, complete graphs have the minimum cover time $N\log
N$. However, complete graphs cannot mimic real-world networks with small
average degree and scale-free small-world properties, for which the cover time
has not been examined carefully, and its behavior is still not well understood.
In this paper, we first experimentally evaluate the cover time for various
real-world networks with scale-free small-world properties, which scales as
$N\log N$. To better understand the behavior of the cover time for real-world
networks, we then study the cover time of three scale-free small-world model
networks by using the connection between cover time and resistance diameter.
For all the three networks, their cover time also behaves as $N\log N$. This
work indicates that sparse networks with scale-free and small-world topology
are favorable architectures with optimal scaling of cover time. Our results
deepen understanding the behavior of cover time in real-world networks with
scale-free small-world structure, and have potential implications in the design
of efficient algorithms related to cover time.
