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Dynamic pattern evolution on scale-free networks.

ABSTRACT: A general class of dynamic models on scale-free networks is studied by analytical methods and computer simulations. Each network consists of N vertices and is characterized by its degree distribution, P(k), which represents the probability that a randomly chosen vertex is connected to k nearest neighbors. Each vertex can attain two internal states described by binary variables or Ising-like spins that evolve in time according to local majority rules. Scale-free networks, for which the degree distribution has a power law tail P(k) approximately k(-gamma), are shown to exhibit qualitatively different dynamic behavior for gamma < 5/2 and gamma > 5/2, shedding light on the empirical observation that many real-world networks are scale-free with 2 < gamma < 5/2. For 2 < gamma < 5/2, strongly disordered patterns decay within a finite decay time even in the limit of infinite networks. For gamma > 5/2, on the other hand, this decay time diverges as ln(N) with the network size N. An analogous distinction is found for a variety of more complex models including Hopfield models for associative memory networks. In the latter case, the storage capacity is found, within mean field theory, to be independent of N in the limit of large N for gamma > 5/2 but to grow as N(alpha) with alpha = (5 - 2gamma)/(gamma - 1) for 2 < gamma < 5/2.

SUBMITTER: Zhou H

PROVIDER: S-EPMC1174918 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Many complex random networks have been found to be scale-free. Existing literature on scale-free networks has rarely considered potential false positive and false negative links in the observed networks, especially in biological networks inferred from high-throughput experiments. Therefore, it is important to study the impact of these measurement errors on the topology of the observed networks.This article addresses the impact of erroneous links on network topological inference and explores possible error mechanisms for scale-free networks with an emphasis on Saccharomyces cerevisiae protein interaction networks. We study this issue by both theoretical derivations and simulations. We show that the ignorance of erroneous links in network analysis may lead to biased estimates of the scale parameter and recommend robust estimators in such scenarios. Possible error mechanisms of yeast protein interaction networks are explored by comparisons between real data and simulated data.Our studies show that, in the presence of erroneous links, the connectivity distribution of scale-free networks is still scale-free for the middle range connectivities, but can be greatly distorted for low and high connecitivities. It is more appropriate to use robust estimators such as the least trimmed mean squares estimator to estimate the scale parameter gamma under such circumstances. Moreover, we show by simulation studies that the scale-free property is robust to some error mechanisms but untenable to others. The simulation results also suggest that different error mechanisms may be operating in the yeast protein interaction networks produced from different data sources. In the MIPS gold standard protein interaction data, there appears to be a high rate of false negative links, and the false negative and false positive rates are more or less constant across proteins with different connectivities. However, the error mechanism of yeast two-hybrid data may be very different, where the overall false negative rate is low and the false negative rates tend to be higher for links involving proteins with more interacting partners.

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Dynamic pattern evolution on scale-free networks.

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