Many communication and social networks have power-law link distributions, containing a few nodes which have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact which can be exploited when designing efficient search algorithms. We introduce a number of local search strategies which utilize high degree nodes in power-law graphs and which have costs which scale sub-linearly with the size of the graph. We also demonstrate the utility of these strategies on the Gnutella peer-to-peer network. A number of large distributed systems, ranging from social [13] to communication [11] to biological networks [9] display a power-law distribution in their node degree. This distribution reflects the existence of a few nodes with very high degree and many with low degree, a feature not found in standard random graphs [5] . An illustration of the power-law nature of such networks is given by the AT&T call graph. A call graph is a graph representation of telephone traffic on a given day in which nodes represent people and links the phone calls among them. As is shown in Figure 1 , the out-link degree distribution for a massive graph of telephone calls between individuals is power-law, with an exponent of approximately 2.1. The same distribution is obtained for the case of in-links. This power-law in the link distribution reflects the presence of central individuals who interact with many others on a daily basis and play a key role in relaying information. While recent work has concentrated on the properties of these power-law networks and how they are dynamically generated [2, 8, 12] , there remains the interesting problem of finding efficient *
For random walk-based strategies the work in REF introduces a number of local search strategies that utilize high degree peers in power-law graphs and that have costs scaling sublinearly with the size of the graph.
Search in Power-Law Networks
Phys. Rev. E 64, 046135 (2001)
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