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.

Google matrix analysis of directed networks

In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency on various examples including World Wide Web, Wikipedia, software architecture, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory.Comment: 56 pages, 58 figures. Missed link added in network example of Fig3

Usage Bibliometrics

Scholarly usage data provides unique opportunities to address the known shortcomings of citation analysis. However, the collection, processing and analysis of usage data remains an area of active research. This article provides a review of the state-of-the-art in usage-based informetric, i.e. the use of usage data to study the scholarly process.Comment: Publisher's PDF (by permission). Publisher web site: books.infotoday.com/asist/arist44.shtm

Software tools for conducting bibliometric analysis in science: An up-to-date review

Bibliometrics has become an essential tool for assessing and analyzing the output of scientists, cooperation between universities, the effect of state-owned science funding on national research and development performance and educational efficiency, among other applications. Therefore, professionals and scientists need a range of theoretical and practical tools to measure experimental data. This review aims to provide an up-to-date review of the various tools available for conducting bibliometric and scientometric analyses, including the sources of data acquisition, performance analysis and visualization tools. The included tools were divided into three categories: general bibliometric and performance analysis, science mapping analysis, and libraries; a description of all of them is provided. A comparative analysis of the database sources support, pre-processing capabilities, analysis and visualization options were also provided in order to facilitate its understanding. Although there are numerous bibliometric databases to obtain data for bibliometric and scientometric analysis, they have been developed for a different purpose. The number of exportable records is between 500 and 50,000 and the coverage of the different science fields is unequal in each database. Concerning the analyzed tools, Bibliometrix contains the more extensive set of techniques and suitable for practitioners through Biblioshiny. VOSviewer has a fantastic visualization and is capable of loading and exporting information from many sources. SciMAT is the tool with a powerful pre-processing and export capability. In views of the variability of features, the users need to decide the desired analysis output and chose the option that better fits into their aims

The Research Space: using the career paths of scholars to predict the evolution of the research output of individuals, institutions, and nations

In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps