Network heterogeneity and node capacity lead to heterogeneous scaling of fluctuations in random walks on graphs
| Autor: | Kosmidis, Kosmas, Beber, Moritz, Hütt, Marc-Thorsten |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Advances in Complex Systems, 1550007, 2015 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0219525915500071 |
| Popis: | Random walks are one of the best investigated dynamical processes on graphs. A particularly fascinating phenomenon is the scaling relationship of fluctuations $\sigma $ with the average flux $\langle f \rangle $. Here we analyze how network topology and nodes with finite capacity lead to deviations from a simple scaling law $\sigma \sim \langle f \rangle ^\alpha$. Sources of randomness are the random walk itself (internal noise) and the fluctuation of the number of walkers (external noise). We obtained exact results for the extreme case of a star network which are indicative of the behavior of large scale systems with a broad degree distribution.The latter are subsequently studied using Monte Carlo simulations. We find that the network heterogeneity amplifies the effects of external noise. By computing the `effective' scaling of each node we show that multiple scaling relationships can coexist in a graph with a heterogeneous degree distribution at an intermediate level of external noise. Finally, we analyze the effect of a finite capacity of nodes for random walkers and find that this also can lead to a heterogeneous scaling of fluctuations. Comment: 12 pages, 11 figures |
| Databáze: | arXiv |
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