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A key element to understand complex systems is the relationship between the spatial scale of investigation and the structure of the interrelation among its elements. When it comes to economic systems, it is now well-known that the country-product bipartite network exhibits a nested structure, which is the foundation of different algorithms that have been used to scientifically investigate countries' development and forecast national economic growth. Changing the subject from countries to companies, a significantly different scenario emerges. Through the analysis of a unique dataset of Italian firms' exports and a worldwide dataset comprising countries' exports, here we find that, while a globally nested structure is observed at the country level, a local, in-block nested structure emerges at the level of firms. Remarkably, this in-block nestedness is statistically significant with respect to suitable null models and the algorithmic partitions of products into blocks have a high correspondence with exogenous product classifications. These findings lay a solid foundation for developing a scientific approach based on the physics of complex systems to the analysis of companies, which has been lacking until now.

Scientific and technological progress is largely driven by firms in many domains, including artificial intelligence and vaccine development. However, we do not know yet whether the success of firms' research activities exhibits dynamic regularities and some degree of predictability. By inspecting the research lifecycles of 7,440 firms, we find that the economic value of a firm's early patents is an accurate predictor of various dimensions of a firm's future research success. At the same time, a smaller set of future top-performers do not generate early patents of high economic value, but they are detectable via the technological value of their early patents. Importantly, the observed predictability cannot be explained by a cumulative advantage mechanism, and the observed heterogeneity of the firms' temporal success patterns markedly differs from patterns previously observed for individuals' research careers. Our results uncover the dynamical regularities of the research success of firms, and they could inform managerial strategies as well as policies to promote entrepreneurship and accelerate human progress., Comment: 15 pages,7 figures

Networks representing complex systems in nature and society usually involve multiple interaction types. These types suggest essential information on the interactions between components, but not all of the existing types are usually discovered. Therefore, detecting the undiscovered edge types is crucial for deepening our understanding of the network structure. Although previous studies have discussed the edge label detection problem, we still lack effective methods for uncovering previously-undetected edge types. Here, we develop an effective technique to detect undiscovered new edge types in networks by leveraging a novel temporal network model. Both analytical and numerical results show that the prediction accuracy of our method is perfect when the model networks' time parameter approaches infinity. Furthermore, we find that when time is finite, our method is still significantly more accurate than the baseline.

With vast amounts of high-quality information at our fingertips, how is it possible that many people believe that the Earth is flat and vaccination harmful? Motivated by this question, we quantify the implications of an opinion formation mechanism whereby an uninformed observer gradually forms opinions about a world composed of subjects interrelated by a signed network of mutual trust and distrust. We show numerically and analytically that the observer's resulting opinions are highly inconsistent (they tend to be independent of the observer's initial opinions) and unstable (they exhibit wide stochastic variations). Opinion inconsistency and instability increase with the world complexity represented by the number of subjects, which can be prevented by suitably expanding the observer's initial amount of information. Our findings imply that even an individual who initially trusts credible information sources may end up trusting the deceptive ones if at least a small number of trust relations exist between the credible and deceptive sources., Comment: 12 pages, 7 figures plus Supporting Material

Ranking algorithms are pervasive in our increasingly digitized societies, with important real-world applications including recommender systems, search engines, and influencer marketing practices. From a network science perspective, network-based ranking algorithms solve fundamental problems related to the identification of vital nodes for the stability and dynamics of a complex system. Despite the ubiquitous and successful applications of these algorithms, we argue that our understanding of their performance and their applications to real-world problems face three fundamental challenges: (i) Rankings might be biased by various factors; (2) their effectiveness might be limited to specific problems; and (3) agents' decisions driven by rankings might result in potentially vicious feedback mechanisms and unhealthy systemic consequences. Methods rooted in network science and agent-based modeling can help us to understand and overcome these challenges., Comment: Perspective article. 9 pages, 3 figures

Originally a speculative pattern in ecological networks, the hybrid or compound nested-modular pattern has been confirmed, during the last decade, as a relevant structural arrangement that emerges in a variety of contexts --in ecological mutualistic system and beyond. This implies shifting the focus from the measurement of nestedness as a global property (macro level), to the detection of blocks (meso level) that internally exhibit a high degree of nestedness. Unfortunately, the availability and understanding of the methods to properly detect in-block nested partitions lie behind the empirical findings: while a precise quality function of in-block nestedness has been proposed, we lack an understanding of its possible inherent constraints. Specifically, while it is well known that Newman-Girvan's modularity, and related quality functions, notoriously suffer from a resolution limit that impairs their ability to detect small blocks, the potential existence of resolution limits for in-block nestedness is unexplored. Here, we provide empirical, numerical and analytical evidence that the in-block nestedness function lacks a resolution limit, and thus our capacity to detect correct partitions in networks via its maximization depends solely on the accuracy of the optimization algorithms., Comment: 12 pages, 4 figures, 1 table

Online news can quickly reach and affect millions of people, yet we do not know yet whether there exist potential dynamical regularities that govern their impact on the public. We use data from two major news outlets, BBC and New York Times, where the number of user comments can be used as a proxy of news impact. We find that the impact dynamics of online news articles does not exhibit popularity patterns found in many other social and information systems. In particular, we find that a simple exponential distribution yields a better fit to the empirical news impact distributions than a power-law distribution. This observation is explained by the lack or limited influence of the otherwise omnipresent rich-get-richer mechanism in the analyzed data. The temporal dynamics of the news impact exhibits a universal exponential decay which allows us to collapse individual news trajectories into an elementary single curve. We also show how daily variations of user activity directly influence the dynamics of the article impact. Our findings challenge the universal applicability of popularity dynamics patterns found in other social contexts., Comment: 11 pages, 6 figures + Supporting Information (18 pages, 16 figures)

Can we predict top-performing products, services, or businesses by only monitoring the behavior of a small set of individuals? Although most previous studies focused on the predictive power of "hub" individuals with many social contacts, which sources of customer behavioral data are needed to address this question remains unclear, mostly due to the scarcity of available datasets that simultaneously capture individuals' purchasing patterns and social interactions. Here, we address this question in a unique, large-scale dataset that combines individuals' credit-card purchasing history with their social and mobility traits across an entire nation. Surprisingly, we find that the purchasing history alone enables the detection of small sets of ``discoverers" whose early purchases offer reliable success predictions for the brick-and-mortar stores they visit. In contrast with the assumptions by most existing studies on word-of-mouth processes, the hubs selected by social network centrality are not consistently predictive of success. Our findings show that companies and organizations with access to large-scale purchasing data can detect the discoverers and leverage their behavior to anticipate market trends, without the need for social network data., Comment: Main text (pp. 1-13), Online appendix (pp. 14-34)

Time-stamped data are increasingly available for many social, economic, and information systems that can be represented as networks growing with time. The World Wide Web, social contact networks, and citation networks of scientific papers and online news articles, for example, are of this kind. Static methods can be inadequate for the analysis of growing networks as they miss essential information on the system's dynamics. At the same time, time-aware methods require the choice of an observation timescale, yet we lack principled ways to determine it. We focus on the popular community detection problem which aims to partition a network's nodes into meaningful groups. We use a multi-layer quality function to show, on both synthetic and real datasets, that the observation timescale that leads to optimal communities is tightly related to the system's intrinsic aging timescale that can be inferred from the time-stamped network data. The use of temporal information leads to drastically different conclusions on the community structure of real information networks, which challenges the current understanding of the large-scale organization of growing networks. Our findings indicate that before attempting to assess structural patterns of evolving networks, it is vital to uncover the timescales of the dynamical processes that generated them., Comment: 14 pages, 8 figures + Supplementary Material

As new instances of nested organization --beyond ecological networks-- are discovered, scholars are debating around the co-existence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being solved, mainly for two reasons. First, nestedness and modularity appear to emerge from two contradictory dynamics, cooperation and competition. Second, existing methods to assess the presence of nestedness and modularity are flawed when it comes to the evaluation of concurrently nested and modular structures. In this work, we tackle the latter problem, presenting the concept of \textit{in-block nestedness}, a structural property determining to what extent a network is composed of blocks whose internal connectivity exhibits nestedness. We then put forward a set of optimization methods that allow us to identify such organization successfully, both in synthetic and in a large number of real networks. These findings challenge our understanding of the topology of ecological and social systems, calling for new models to explain how such patterns emerge., Comment: 16 pages, 5 figures, 1 Table

The dynamics of individuals is of essential importance for understanding the evolution of social systems. Most existing models assume that individuals in diverse systems, ranging from social networks to e-commerce, all tend to what is already popular. We develop an analytical time-aware framework which shows that when individuals make choices -- which item to buy, for example -- in online social systems, a small fraction of them is consistently successful in discovering popular items long before they actually become popular. We argue that these users, whom we refer to as discoverers, are fundamentally different from the previously known opinion leaders, influentials, and innovators. We use the proposed framework to demonstrate that discoverers are present in a wide range of systems. Once identified, they can be used to predict the future success of items. We propose a network model which reproduces the discovery patterns observed in the real data. Furthermore, data produced by the model pose a fundamental challenge to classical ranking algorithms which neglect the time of link creation and thus fail to discriminate between discoverers and ordinary users in the data. Our results open the door to qualitative and quantitative study of fine temporal patterns in social systems and have far-reaching implications for network modeling and algorithm design., Comment: main paper (11 pages, 5 figures) together with supporting information (8 pages, 6 figures)