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Analysis of institutional authors

Martin-Gutierrez, SamuelAuthor
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Variance and Covariance of Distributions on Graphs

Publicated to:Siam Review. 64 (2): 343-359 - 2022-01-01 64(2), DOI: 10.1137/20M1361328

Authors: Devriendt K; Martin-Gutierrez S; Lambiotte R

Affiliations

Alan Turing Inst, London, England - Author
Complex Sci Hub Vienna, Network Inequal Grp, Vienna, Austria - Author
Univ Oxford, Math Inst, Oxford, England - Author
Univ Politecn Madrid, Grp Sistemas Complejos, Escuela Tecn Super Ingn Agron Alimentaria & Biosi, Madrid, Spain - Author

Abstract

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of weighted graphs and retains many of its intuitive and desired properties. Interestingly, we find that a number of famous concepts in graph theory and network science can be reinterpreted in this setting as variances and covariances of particular distributions. As a particular application, we define the maximum variance problem on graphs with respect to the effective resistance distance, and we characterize the solutions to this problem both numerically and theoretically. We show how the maximum variance distribution is concentrated on the boundary of the graph, and illustrate this in the case of random geometric graphs. Our theoretical results are supported by a number of experiments on a network of mathematical concepts, where we use the variance and covariance as analytical tools to study the (co)occurrence of concepts in scientific papers with respect to the (network) relations between these concepts.

Keywords
bibliographic networkdiversity measureeffective resistancegeometric networkvariance and covariancewikipedia networkBibliographic networkDiversity measureEffective resistanceFunctional diversityGeometric networkNetwork analysisVariance and covarianceWikipedia network

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Siam Review due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position 1/267, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.03. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.52 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 11.07 (source consulted: Dimensions May 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-05-17, the following number of citations:

  • WoS: 4
  • Scopus: 12
  • Google Scholar: 18
  • OpenCitations: 10
Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-05-17:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 42.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 42 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.5.
  • The number of mentions on the social network X (formerly Twitter): 3 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Austria; United Kingdom.