Diffusive processes describe a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here  we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks , and to recognize the concept of an annealed weighted network , in which such equations become exact. The analysis of the simple random walk process reveals a strong departure of its behavior in quenched real scale-free networks from the mean-field predictions.  Our work sheds light on mean-field theory on weighted networks and on its range of validity, warning about the reliability of mean-field results for more complex dynamics.
Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here , we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks . We also propose the concept of annealed weighted networks , in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process , pointing out a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions. Additionally, we show how to employ our formalism for more complex dynamics. Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for complex dynamics.
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Diffusive processes describe a
Diffusion is a key element of a
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,
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, and to recognize
. We also propose
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an annealed weighted network
annealed weighted networks
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The analysis of the simple
We show the validity of our approach addressing the problem of the
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reveals
, pointing out
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its behavior
the behavior observed
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Additionally, we show how to employ our formalism for more complex dynamics.
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warning
and warns
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more