Citation networks have re-emerged as a topic intense interest in the complex networks community with the recent availability of large-scale data sets. The ranking of citation networks is a necessary practice as a means to improve information navigability and search. Unlike many information networks, the aging characteristics of citation networks require the development of new ranking methods. To account for strong aging characteristics of citation networks, we modify the PageRank algorithm by initially distributing random surfers exponentially with age, in favor of more recent publications. The output of this algorithm, which we call CiteRank, is interpreted as approximate traffic to individual publications in a simple model of how researchers find new information. We optimize parameters of our algorithm to achieve the best performance. The results are compared for two rather different citation networks: all American Physical Society publications between 1893-2003 and the set of high-energy physics theory (hep-th) preprints. Despite major differences between these two networks, we find that their optimal parameters for the CiteRank algorithm are remarkably similar. The advantages and performance of CiteRank over more conventional methods of ranking publications are discussed.

Collaborative voting systems have emerged as an abundant form of real-world, complex information systems that exist in a variety of online applications. These systems are comprised of large populations of users that collectively submit and vote on objects. While the specific properties of these systems vary widely, many of them share a core set of features and dynamical behaviors that govern their evolution. We study a subset of these systems that involve material of a time-critical nature as in the popular example of news items. We consider a general model system in which articles are introduced, voted on by a population of users, and subsequently expire after a proscribed period of time. To study the interaction between popularity and quality, we introduce simple stochastic models of user behavior that approximate differing user quality and susceptibility to the common notion of popularity. We define a metric to quantify user reputation in a manner that is self-consistent, adaptable and content-blind and shows good correlation with the probability that a user behaves in an optimal fashion. We further construct a mechanism for ranking documents that take into account user reputation and provides substantial improvement in the time-critical performance of the system.

The structure of complex systems have been well studied in the context of both information and biological systems. More recently, dynamics in complex systems that occur over the background of the underlying network has received a great deal of attention. In particular, the study of fluctuations in complex systems has emerged as an issue central to understanding dynamical behavior. We approach the problem of collective effects of the underlying network on dynamical fluctuations by considering the protein-protein interaction networks for the system of the living cell. We consider two types of fluctuations in the mass-action equilibrium in protein binding networks. The first type is driven by relatively slow changes in total concentrations (copy numbers) of interacting proteins. The second type, to which we refer to as spontaneous, is caused by quickly decaying thermodynamic deviations away from the mass-action equilibrium of the system. As such they are amenable to methods of equilibrium statistical mechanics used in our study. We investigate the effects of network connectivity on these fluctuations by comparing them to different scenarios in which the interacting pair is isolated form the rest of the network. Such comparison allows us to analytically derive upper and lower bounds on network fluctuations. The collective effects are shown to sometimes lead to relatively large amplification of spontaneous fluctuations as compared to the expectation for isolated dimers. As a consequence of this, the strength of both types of fluctuations is positively correlated with the overall network connectivity of proteins forming the complex. On the other hand, the relative amplitude of fluctuations is negatively correlated with the equilibrium concentration of the complex. Our general findings are illustrated using a curated network of protein-protein interactions and multi-protein complexes in bakers yeast with experimentally determined protein concentrations.