  Overlay network topology together with peer/data organization and search
algorithm are the crucial components of unstructured peer-to-peer (P2P)
networks as they directly affect the efficiency of search on such networks.
Scale-free (powerlaw) overlay network topologies are among structures that
offer high performance for these networks. A key problem for these topologies
is the existence of hubs, nodes with high connectivity. Yet, the peers in a
typical unstructured P2P network may not be willing or able to cope with such
high connectivity and its associated load. Therefore, some hard cutoffs are
often imposed on the number of edges that each peer can have, restricting
feasible overlays to limited or truncated scale-free networks. In this paper,
we analyze the growth of such limited scale-free networks and propose two
different algorithms for constructing perfect scale-free overlay network
topologies at each instance of such growth. Our algorithms allow the user to
define the desired scalefree exponent (gamma). They also induce low
communication overhead when network grows from one size to another. Using
extensive simulations, we demonstrate that these algorithms indeed generate
perfect scale free networks (at each step of network growth) that provide
better search efficiency in various search algorithms than the networks
generated by the existing solutions.
