Navigation in Social Networks: Inspired by Kleinberg’s Model and Human Travel Behavior Research
چکیده
Though the phenomenon of ’six degrees of separation’ always attracts many scientists’ attention, yet we haven’t thoroughly understood why our social network has such highly efficient decentralized search ability. Inspired by Kleinberg’s model and the fact that human travel behavior obeying power law distribution in the sense of geographical distance, we constructed a new social network model and investigated its search ability. A L × L square lattice is also employed as the ground regular network. Then for each node in the lattice, we randomly add long-range connections according to power law distribution in the lattice distance. We find that for any k-dimensional lattice, only when the exponent of the power law distribution of long-range connection is −1 will the small world network search ability reach the maximum for sufficiently large lattice, and the time complexity is O(ln(L)). This model not only presents a deeper insight of ’six degrees of separation’, but also provides potential applications for the future Internet, WWW, and P2P network etc.