Peer-to-Peer Netw. Appl. (2011) 4:92–105 DOI 10.1007/s12083-010-0067-1 Ad-hoc limited scale-free models for unstructured peer-to-peer networks Durgesh Rani Kumari · Hasan Guclu · Murat Yuksel Received: 29 November 2008 / Accepted: 9 March 2010 / Published online: 9 May 2010 © Springer Science+Business Media, LLC 2010 Abstract Several protocol efficiency metrics (e.g., scal- ability, search success rate, routing reachability and stability) depend on the capability of preserving struc- ture even over the churn caused by the ad-hoc nodes joining or leaving the network. Preserving the structure becomes more prohibitive due to the distributed and potentially uncooperative nature of such networks, as in the peer-to-peer (P2P) networks. Thus, most prac- tical solutions involve unstructured approaches while attempting to maintain the structure at various levels of protocol stack. The primary focus of this paper is to investigate construction and maintenance of scale-free topologies in a distributed manner without requiring global topology information at the time when nodes join or leave. We consider the uncooperative behavior An earlier version of this work appeared in IEEE International Conference on Peer-to-Peer Computing (P2P), 2008. D. R. Kumari (B ) · M. Yuksel Computer Science & Engineering Dept., University of Nevada—Reno, Reno, NV 89557, USA e-mail: dkumari@cse.unr.edu, dkumari@gtiemail.com M. Yuksel e-mail: yuksem@cse.unr.edu H. Guclu School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA e-mail: guclu@rit.edu H. Guclu Computer Science & Engineering Department, Istanbul Sehir University, Istanbul, Turkey e-mail: gucluh@gmail.com of peers by limiting the number of neighbors to a pre- defined hard cutoff value (i.e., no peer is a major hub), and the ad-hoc behavior of peers by rewiring the neigh- bors of nodes leaving the network. We also investigate the effect of these hard cutoffs and rewiring of ad-hoc nodes on the P2P search efficiency. Keywords Scale-free networks · Hard cutoff · Preferential attachment · Power law 1 Introduction Stability and scalability of highly dynamic networks mainly depends on the capability of preserving struc- ture even over the churn caused by the ad-hoc nodes joining or leaving the network. In decentralized peer- to-peer (P2P) networks, the overlay topology (or con- nectivity graph) among peers is a crucial component in addition to the peer/data organization and search. Topological characteristics have profound impact on the efficiency of search on P2P networks as well as other networks. It has been well-known that search on small-world topologies can be as efficient as O(ln N) [27], and this phenomenon has recently been studied on P2P networks [25, 26, 32, 40]. The best search efficiency in realistic networks can be achieved when the topol- ogy is scale-free (power-law), which offers search efficiencies like O(ln ln N). Key limitation of scale-free topologies is the high load (i.e., high degree) on very few number of hub nodes. In a typical unstructured P2P network, peers are not willing to maintain high degrees/loads as they may not want to store large num- ber of entries for construction of the overlay topology.