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

Google matrix of the citation network of Physical Review

We study the statistical properties of spectrum and eigenstates of the Google matrix of the citation network of Physical Review for the period 1893 - 2009. The main fraction of complex eigenvalues with largest modulus is determined numerically by different methods based on high precision computations with up to $p=16384$ binary digits that allows to resolve hard numerical problems for small eigenvalues. The nearly nilpotent matrix structure allows to obtain a semi-analytical computation of eigenvalues. We find that the spectrum is characterized by the fractal Weyl law with a fractal dimension $d_f \approx 1$. It is found that the majority of eigenvectors are located in a localized phase. The statistical distribution of articles in the PageRank-CheiRank plane is established providing a better understanding of information flows on the network. The concept of ImpactRank is proposed to determine an influence domain of a given article. We also discuss the properties of random matrix models of Perron-Frobenius operators.Comment: 25 pages. 17 figures. Published in Phys. Rev.

Popular and/or Prestigious? Measures of Scholarly Esteem

Citation analysis does not generally take the quality of citations into account: all citations are weighted equally irrespective of source. However, a scholar may be highly cited but not highly regarded: popularity and prestige are not identical measures of esteem. In this study we define popularity as the number of times an author is cited and prestige as the number of times an author is cited by highly cited papers. Information Retrieval (IR) is the test field. We compare the 40 leading researchers in terms of their popularity and prestige over time. Some authors are ranked high on prestige but not on popularity, while others are ranked high on popularity but not on prestige. We also relate measures of popularity and prestige to date of Ph.D. award, number of key publications, organizational affiliation, receipt of prizes/honors, and gender.Comment: 26 pages, 5 figure