We study the fluctuation properties and return-time statistics on inhomogeneous scale-free networks using packets moving with two different dynamical rules; random diffusion and locally navigated diffusive motion with preferred edges. Scaling in the fluctuations occurs when the dispersion of a quantity at each node or edge increases like the its mean to the power µ. We show that the occurrence of scaling
Abstract. We present an empirical study of the networks created by users within internet news groups and forums and show that they organise themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. For news groups we find that the distribution of the time intervals between when a message is posted and when it receives a response exhibits a composite power-law behaviour. From our statistics we can see if the news group or forum is free or is overseen by a moderator. The correlation function of activity, the number of messages posted in a given time, shows long range correlations connected with the users' daily routines. The distribution of distances between each message and its root is exponential for most news groups and power-law for the forums. For both formats we find that the relation between the supremacy ( the total number of nodes that are under the node i, including node i) and the degree is linear s(k) ∼ k, in contrast to the analytical relation for Barabási-Albert network.
Abstract. We introduce four algorithms for packet transport in complex networks. These algorithms use deterministic rules which depend, in different ways, on the degree of the node, the number of packets posted down each edge, the mean delivery time of packets sent down each edge to each destination and the time since an edge last transmitted a packet. On scale-free networks all our algorithms are considerably more efficient and can handle a larger load than the random walk algorithm. We consider in detail various attributes of our algorithms, for instance we show that an algorithm that bases its decisions on the mean delivery time jams unless it incorporates information about the degree of the destination node.
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