Guided Search and Distribution of Information Flow on Complex Graphs Bosiljka Tadi´ c Joˇ zef Stefan Institute, Box 3000, 1001 Ljubljana, Slovenia Bosiljka.Tadic ijs.si http://phobos.ijs.si/˜tadic/ Abstract. Within the numerical model proposed in [1] we study the flow of information on a graph with power-law organization of links and an emergent superstructure formed by two highly interconnected hubs. The local search algorithms which navigate transport at each node can use information in the range of zero, one, and two-nearest neighbourhood of the node. We show how the flow carried by a particular link is distributed over graph when range of guided search and posting rate of packets are varied. The probability density function of the flow is given by a universal log-normal law, which is determined by the overall packet density in the stationary traffic. However, the distribution becomes unstable when the traffic experiences temporary or permanent jamming. 1 Introduction The complexity of structure and function of evolving networks is often expressed in emergence of topological communities [2,3,4] and functionally connected units, which are based on the linking properties of the network. The inhomogeneity and sparseness of complex networks effect dynamic processes that these networks support. Recent study of traffic on networks of diverse emergent topologies [1, 5] revels that functional efficiency of a network, however, is not determined by the network’s topology alone, but it also depends on the microscopic rules of the dynamics. In particular, in the transport processes on networks the rules which are adapted to the locally changing networks’ structure lead to more efficient network performance. In the case of random walk dynamics the influence of the structural diversity can be incorporated into search algorithms that navigate the walkers through the graph [6]. Inhomogeneity on the level of local connectivity of nodes makes possible to design variety of navigations rules on complex networks. The requirement for locality of the search is essential for costs reasons. In [1] we have studied two different search algorithms that are guided by locally encountered network struc- ture. It has been found that (a) better guided search leads to better performance of the network; and (b) the same guided search algorithm performs better on networks with higher organizational complexity [1]. An example which illustrates these conclusions is the traffic of information packets on the Web-type graph [7] M. Bubak et al. (Eds.): ICCS 2004, LNCS 3038, pp. 1086–1093, 2004. c  Springer-Verlag Berlin Heidelberg 2004