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D. Markovic and C. Gros A class of models describing the ow of information within net- works via routing processes is proposed and investigated, concentrat- ing on the eects of memory traces on the global properties. The long-term ow of information is governed by cyclic attractors, allow- ing to dene a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We nd the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, nding a complete scaling collapse in the thermodynamic limit for the later. Possible implications of our results on the information ow in social networks are discussed. |
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