Network-based ranking in social systems: three challenges

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 figure

Early identification of important patents through network centrality

One of the most challenging problems in technological forecasting is to identify as early as possible those technologies that have the potential to lead to radical changes in our society. In this paper, we use the US patent citation network (1926-2010) to test our ability to early identify a list of historically significant patents through citation network analysis. We show that in order to effectively uncover these patents shortly after they are issued, we need to go beyond raw citation counts and take into account both the citation network topology and temporal information. In particular, an age-normalized measure of patent centrality, called rescaled PageRank, allows us to identify the significant patents earlier than citation count and PageRank score. In addition, we find that while high-impact patents tend to rely on other high-impact patents in a similar way as scientific papers, the patents' citation dynamics is significantly slower than that of papers, which makes the early identification of significant patents more challenging than that of significant papers.Comment: 14 page

Measuring economic complexity of countries and products: which metric to use?

Evaluating the economies of countries and their relations with products in the global market is a central problem in economics, with far-reaching implications to our theoretical understanding of the international trade as well as to practical applications, such as policy making and financial investment planning. The recent Economic Complexity approach aims to quantify the competitiveness of countries and the quality of the exported products based on the empirical observation that the most competitive countries have diversified exports, whereas developing countries only export few low quality products -- typically those exported by many other countries. Two different metrics, Fitness-Complexity and the Method of Reflections, have been proposed to measure country and product score in the Economic Complexity framework. We use international trade data and a recent ranking evaluation measure to quantitatively compare the ability of the two metrics to rank countries and products according to their importance in the network. The results show that the Fitness-Complexity metric outperforms the Method of Reflections in both the ranking of products and the ranking of countries. We also investigate a Generalization of the Fitness-Complexity metric and show that it can produce improved rankings provided that the input data are reliable

Temporal similarity metrics for latent network reconstruction: The role of time-lag decay

When investigating the spreading of a piece of information or the diffusion of an innovation, we often lack information on the underlying propagation network. Reconstructing the hidden propagation paths based on the observed diffusion process is a challenging problem which has recently attracted attention from diverse research fields. To address this reconstruction problem, based on static similarity metrics commonly used in the link prediction literature, we introduce new node-node temporal similarity metrics. The new metrics take as input the time-series of multiple independent spreading processes, based on the hypothesis that two nodes are more likely to be connected if they were often infected at similar points in time. This hypothesis is implemented by introducing a time-lag function which penalizes distant infection times. We find that the choice of this time-lag strongly affects the metrics' reconstruction accuracy, depending on the network's clustering coefficient and we provide an extensive comparative analysis of static and temporal similarity metrics for network reconstruction. Our findings shed new light on the notion of similarity between pairs of nodes in complex networks

Algorithmic bias amplification via temporal effects: The case of PageRank in evolving networks

Biases impair the effectiveness of algorithms. For example, the age bias of the widely-used PageRank algorithm impairs its ability to effectively rank nodes in growing networks. PageRank’s temporal bias cannot be fully explained by existing analytic results that predict a linear relation between the expected PageRank score and the indegree of a given node. We show that in evolving networks, under a mean-field approximation, the expected PageRank score of a node can be expressed as the product of the node’s indegree and a previously-neglected age factor which can “amplify” the indegree’s age bias. We use two well-known empirical networks to show that our analytic results explain the observed PageRank’s age bias and, when there is an age bias amplification, they enable estimates of the node PageRank score that are more accurate than estimates based solely on local structural information. Accuracy gains are larger in degree-degree correlated networks, as revealed by a growing directed network model with tunable assortativity. Our approach can be used to analytically study other kinds of ranking bias

Calorimetric glass transition in a mean-field theory approach

The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean-field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions; on the experimental and numerical side, the study of the properties of metastable glassy states requires thermalizing the system in the supercooled liquid phase, where the thermalization time may be extremely large. We consider here a hard-sphere mean-field model that is solvable in any number of spatial dimensions; moreover, we easily obtain thermalized configurations even in the glass phase. We study the 3D version of this model and we perform Monte Carlo simulations that mimic heating and cooling experiments performed on ultrastable glasses. The numerical findings are in good agreement with the analytical results and qualitatively capture the features of ultrastable glasses observed in experiments