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Self-loops in Social Networks: Behavior of Eigenvector Centrality

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Artificial Life and Evolutionary Computation (WIVACE 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1977))

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Abstract

Centrality measures are an essential tool in understanding complex networks, since they give researcher insights on the role the different nodes/actors play in them. Among them, eigenvector centrality is a principled approach to these measures, using a mathematical operation on the connection matrix. This connection matrix includes connections from an actor to itself (the diagonal); however, as it is the case with most centrality measures, this fact is seldom used in social studies to compute the standing or influence of one node over others. In this paper we will analyze the difference in EV centrality with or without these self connections or self-loops and how the change depends on the actual number of these self-loops or the weight of these self-connections. Finally, we will characterize in which cases, if any, it is effective to drop self-loops and what kind of information it will give us on the nature and dynamics of the network.

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Notes

  1. 1.

    Some marriages are not dated, but we can assume they took place in the same range of years.

  2. 2.

    Since the dataset includes some marriages that happened after the fall of the Republic in 1796, the concept of “noble” in this case corresponds to families that were considered noble during the existence of the Republic; during French and Austrian control, as well as during the brief period of the Republic of San Marco, such nobility titles no longer had any value; however, since they were included in the original dataset there was no good reason to eliminate them.

  3. 3.

    There were many restrictions to this kind of marriage, but they occurred with regularity, at least until the so-called “Second Serrata” [4], during the XV century; in this case, however, we eliminate them because they are irrelevant to the main point of the paper, not having any influence in the EV centrality of a specific node.

  4. 4.

    The Pisani family is certainly more “central” than the Loredan, at least looking at the number of nobles in important offices; [15] mentions them as one of the family with the greatest amount of shares in shipping contracts.

  5. 5.

    https://www.bts.gov/browse-statistical-products-and-data/state-transportation-statistics/freight-flows-state.

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Acknowledgements

This work is supported by the Ministerio español de Economía y Competitividad (Spanish Ministry of Competitivity and Economy) under project PID2020-115570GB-C22 (DemocratAI::UGR).

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Authors and Affiliations

  1. Department of Computer Engineering, Automatics and Robotics and CITIC University of Granada, Granada, Spain

    J. J. Merelo

  2. Dipartimento di Economia, Ca’ Foscari University of Venice, Venice, Italy

    M. Cristina Molinari

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  1. J. J. Merelo
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  2. M. Cristina Molinari
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Correspondence to J. J. Merelo .

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Editors and Affiliations

  1. University of Modena and Reggio Emilia, Modena, Italy

    Marco Villani

  2. University of Parma, Parma, Italy

    Stefano Cagnoni

  3. University of Modena and Reggio Emilia, Modena, Italy

    Roberto Serra

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Merelo, J.J., Molinari, M.C. (2024). Self-loops in Social Networks: Behavior of Eigenvector Centrality. In: Villani, M., Cagnoni, S., Serra, R. (eds) Artificial Life and Evolutionary Computation. WIVACE 2023. Communications in Computer and Information Science, vol 1977. Springer, Cham. https://doi.org/10.1007/978-3-031-57430-6_28

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  • DOI: https://doi.org/10.1007/978-3-031-57430-6_28

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