Large networks contain plentiful information about the organization of a system. The challenge is to extract useful information buried in the structure of myriad nodes and links. Therefore, powerful tools for simplifying and highlighting important structures in networks are essential for comprehending their organization. Such tools are called community-detection methods and they are designed to identify strongly intraconnected modules that often correspond to important functional units. Here we describe one such method, known as the map equation, and its accompanying algorithms for finding, evaluating, and visualizing the modular organization of networks. The map equation framework is very flexible and can identify two-level, multi-level, and overlapping organization in weighted, directed, and multiplex networks with its search algorithm Infomap. Because the map equation framework operates on the flow induced by the links of a network, it naturally captures flow of ideas and citation flow, and is therefore well-suited for analysis of bibliometric networks.

Abstract:Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-detection algorithms to reveal important modular regularities in the flows. Here we show that various forms of higher-order network flows can be represented in a unified way with networks that distinguish physical nodes for representing a complex system's objects from state nodes for describing flows between the objects. Moreover, these so-called sparse memory networks allow the information-theoretic community detection method known as the map equation to identify overlapping and nested flow modules in data from a range of different higher-order interactions such as multistep, multi-source, and temporal data. We derive the map equation applied to sparse memory networks and describe its search algorithm Infomap, which can exploit the flexibility of sparse memory networks. Together they provide a general solution to reveal overlapping modular patterns in higher-order flows through complex systems.

We live in a global village where electronic communication has eliminated the geographical barriers of information exchange. The road is now open to worldwide convergence of information interests, shared values and understanding. Nevertheless, interests still vary between countries around the world. This raises important questions about what today's world map of information interests actually looks like and what factors cause the barriers of information exchange between countries. To quantitatively construct a world map of information interests, we devise a scalable statistical model that identifies countries with similar information interests and measures the countries' bilateral similarities. From the similarities we connect countries in a global network and find that countries can be mapped into 18 clusters with similar information interests. Through regression we find that language and religion best explain the strength of the bilateral ties and formation of clusters. Our findings provide a quantitative basis for further studies to better understand the complex interplay between shared interests and conflict on a global scale. The methodology can also be extended to track changes over time and capture important trends in global information exchange.

Although the understanding of and motivation behind individual trading behavior is an important puzzle in finance, little is known about the connection between an investor's portfolio structure and her trading behavior in practice. In this paper, we investigate the relation between what stocks investors hold, and what stocks they buy, and show that investors with similar portfolio structures to a great extent trade in a similar way. With data from the central register of shareholdings in Sweden, we model the market in a similarity network, by considering investors as nodes, connected with links representing portfolio similarity. From the network, we find investor groups that not only identify different investment strategies, but also represent individual investors trading in a similar way. These findings suggest that the stock portfolios of investors hold meaningful information, which could be used to earn a better understanding of stock market dynamics.

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 with influence from 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. Here we compare the robustness of three journal rankings based on network flows induced on citation networks. They model pathways of researchers navigating scholarly literature, stepping between journals and remembering their previous steps to different degree: 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 the secondorder Markov model comes at the cost of requiring more citation data over a longer time period.Science builds on previous science in a recursive quest for new knowledge (1-3). Researchers put great effort into finding the best work by other researchers and into achieving maximum visibility of their own work. Therefore, they both search for good work and seek to publish in prominent journals. Inevitably, where researchers publish becomes a proxy for how good their work is, which in turn influences decisions regarding hiring, promotion, and tenure, as well as university rankings and academic funding (4, 5). As a consequence, researchers depend on the perceived importance of the journals they publish in. While actually reading the work published in a journal is the only way to qualitatively evaluate the scientific content, different metrics are nevertheless used to quantitatively assess the importance of scientific journals (6-13). In different ways, the metrics extract information from the network of citations between articles published in the journals.In this paper, we analyze three flow-based journal rankings (12-14) that at different order of approximations seek to capture the pathways of researchers navigating scholarly literature. Specifically, the metrics measure the journal visit frequency of random walk processes that correspond to zero-, first-, and second-order Markov models. That is, given a citation network between journals and a random walker following the citations, movements in a zero-order model are independent of the cur- * Electronic address: ludvig.bohlin@physics.umu.se; Corresponding author † Electronic address: a.viamontes.esquivel@physics.umu.se ‡ Electronic address: andrea.lancichinetti@physics.umu.se § Electronic address: martin.rosvall@physics.umu.se rently visited journal, moveme...