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As the number of scientific journals has multiplied, journal rankings have become increasingly important for scientific decisions. From submissions and subscriptions to grants and hirings, researchers, policy makers, and funding agencies make important decisions influenced by journal rankings such as the ISI journal impact factor. Typically, the rankings are derived from the citation network between a selection of journals and unavoidably depend on this selection. However, little is known about how robust rankings are to the selection of included journals. We compare the robustness of three journal rankings based on network flows induced on citation networks. They model pathways of researchers navigating the scholarly literature, stepping between journals and remembering their previous steps to different degrees: zero-step memory as impact factor, one-step memory as Eigenfactor, and two-step memory, corresponding to zero-, first-, and second-order Markov models of citation flow between journals. We conclude that higher-order Markov models perform better and are more robust to the selection of journals. Whereas our analysis indicates that higher-order models perform better, the performance gain for higher-order Markov models comes at the cost of requiring more citation data over a longer time period.

To better understand the inner workings of information spreading, network researchers often use simple models to capture the spreading dynamics. But most models only highlight the effect of local interactions on the global spreading of a single information wave, and ignore the effects of interactions between multiple waves. Here we take into account the effect of multiple interacting waves by using an agent-based model in which the interaction between information waves is based on their novelty. We analyzed the global effects of such interactions and found that information that actually reaches nodes reaches them faster. This effect is caused by selection between information waves: lagging waves die out and only leading waves survive. As a result, and in contrast to models with noninteracting information dynamics, the access to information decays with the distance from the source. Moreover, when we analyzed the model on various synthetic and real spatial road networks, we found that the decay rate also depends on the path redundancy and the effective dimension of the system. In general, the decay of the information wave frequency as a function of distance from the source follows a power-law distribution with an exponent between -0.2 for a two-dimensional system with high path redundancy and -0.5 for a tree-like system with no path redundancy. We found that the real spatial networks provide an infrastructure for information spreading that lies in between these two extremes. Finally, to better understand the mechanics behind the scaling results, we provide analytical calculations of the scaling for a one-dimensional system.

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markovapproach is used in conventional community detection, ranking, and spreading analysis although it ignores a potentially important feature ofthe dynamics: where flow moves to may depend on where it comes from. Here we analyse pathways from different systems, and while weonly observe marginal consequences for disease spreading, we show that ignoring the effects of second-order Markov dynamics has importantconsequences for community detection, ranking, and information spreading. For example, capturing dynamics with a second-order Markovmodel allows us to reveal actual travel patterns in air traffic and to uncover multidisciplinary journals in scientific communication. Thesefindings were achieved only by using more available data and making no additional assumptions, and therefore suggest that accounting forhigher-order memory in network flows can help us better understand how real systems are organized and function.

To better understand the organization of overlapping modules in large networks with respect to flow, we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between compression and regularity detection. The generalized map equation measures how well we can compress a description of flow in the network when we partition it into modules with possible overlaps. When we minimize the generalized map equation over overlapping network partitions, we detect modules that capture flow and determine which nodes at the boundaries between modules should be classified in multiple modules and to what degree. With a novel greedy-search algorithm, we find that some networks, for example, the neural network of the nematode Caenorhabditis elegans, are best described by modules dominated by hard boundaries, but that others, for example, the sparse European-roads network, have an organization of highly overlapping modules.