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The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two seemingly unrelat ed subjects, are revealed in this paper to be both highly dependent on the critical links previously thought to only be able to influence the number of driver nodes in controllable directed networks. Here, we show that critical links can not only contribute to structural controllability, but they can also have a significant impact on the structural predictability of networks, suggesting the universal pattern of structural reciprocity in directed networks. In addition, it is shown that the fraction and location of critical links have a strong influence on the performance of prediction algorithms. Moreover, these empirical results are interpreted by introducing the link centrality based on corresponding line graphs. This work bridges the gap between the two independent research fields, and it provides indications of developing advanced control strategies and prediction algorithms from a microscopic perspective.
While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to calibrate a state- of-art model for synthetic sports results. Model data are then used to assess the ranking performance of PageRank in a controlled setting. We find that PageRank outperforms the benchmark ranking by the number of wins only when a small fraction of all games have been played. Increased randomness in the data, such as intrinsic randomness of outcomes or advantage of home teams, further reduces the range of PageRanks superiority. We propose a new PageRank variant which outperforms PageRank in all evaluated settings, yet shares its sensitivity to increased randomness in the data. Our main findings are confirmed by evaluating the ranking algorithms on real data. Our work demonstrates the danger of using novel metrics and algorithms without considering their limits of applicability.
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 systems 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 networks 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 systems 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.
Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its r elevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.
We introduce a fully probabilistic framework of consumer product choice based on quality assessment. It allows us to capture many aspects of marketing such as partial information asymmetry, quality differentiation, and product placement in a supermarket.
Using heat conduction mechanism on a social network we develop a systematic method to predict missing values as recommendations. This method can treat very large matrices that are typical of internet communities. In particular, with an innovative, ex act formulation that accommodates arbitrary boundary condition, our method is easy to use in real applications. The performance is assessed by comparing with traditional recommendation methods using real data.
Information overload in the modern society calls for highly efficient recommendation algorithms. In this letter we present a novel diffusion based recommendation model, with users ratings built into a transition matrix. To speed up computation we int roduce a Green function method. The numerical tests on a benchmark database show that our prediction is superior to the standard recommendation methods.
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