The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks
Abstract Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a g...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-10-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-22798-6 |
| _version_ | 1811197963970543616 |
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| author | Massimo Bernaschi Alessandro Celestini Stefano Guarino Enrico Mastrostefano Fabio Saracco |
| author_facet | Massimo Bernaschi Alessandro Celestini Stefano Guarino Enrico Mastrostefano Fabio Saracco |
| author_sort | Massimo Bernaschi |
| collection | DOAJ |
| description | Abstract Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a given population. In the present paper, we introduce the Fitness-Corrected Block Model, an adjustable-density variation of the well-known Degree-Corrected Block Model, and we show that the proposed construction yields a maximum entropy model. When the network is sparse, we derive an analytical expression for the degree distribution of the model that depends on just the constraints and the chosen fitness-distribution. Our model is perfectly suited to define maximum-entropy data-driven spatial social networks, where each block identifies vertices having similar position (e.g., residence) and age, and where the expected block-to-block adjacency matrix can be inferred from the available data. In this case, the sparse-regime approximation coincides with a phenomenological model where the probability of a link binding two individuals is directly proportional to their sociability and to the typical cohesion of their age-groups, whereas it decays as an inverse-power of their geographic distance. We support our analytical findings through simulations of a stylized urban area. |
| first_indexed | 2024-04-12T01:23:20Z |
| format | Article |
| id | doaj.art-84510bf57a6a456ba14944bf490f0abd |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-12T01:23:20Z |
| publishDate | 2022-10-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-84510bf57a6a456ba14944bf490f0abd2022-12-22T03:53:43ZengNature PortfolioScientific Reports2045-23222022-10-0112111210.1038/s41598-022-22798-6The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networksMassimo Bernaschi0Alessandro Celestini1Stefano Guarino2Enrico Mastrostefano3Fabio Saracco4Institute for Applied Computing “Mauro Picone”, National Research Council of ItalyInstitute for Applied Computing “Mauro Picone”, National Research Council of ItalyInstitute for Applied Computing “Mauro Picone”, National Research Council of ItalyInstitute for Applied Computing “Mauro Picone”, National Research Council of ItalyInstitute for Applied Computing “Mauro Picone”, National Research Council of ItalyAbstract Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a given population. In the present paper, we introduce the Fitness-Corrected Block Model, an adjustable-density variation of the well-known Degree-Corrected Block Model, and we show that the proposed construction yields a maximum entropy model. When the network is sparse, we derive an analytical expression for the degree distribution of the model that depends on just the constraints and the chosen fitness-distribution. Our model is perfectly suited to define maximum-entropy data-driven spatial social networks, where each block identifies vertices having similar position (e.g., residence) and age, and where the expected block-to-block adjacency matrix can be inferred from the available data. In this case, the sparse-regime approximation coincides with a phenomenological model where the probability of a link binding two individuals is directly proportional to their sociability and to the typical cohesion of their age-groups, whereas it decays as an inverse-power of their geographic distance. We support our analytical findings through simulations of a stylized urban area.https://doi.org/10.1038/s41598-022-22798-6 |
| spellingShingle | Massimo Bernaschi Alessandro Celestini Stefano Guarino Enrico Mastrostefano Fabio Saracco The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks Scientific Reports |
| title | The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks |
| title_full | The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks |
| title_fullStr | The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks |
| title_full_unstemmed | The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks |
| title_short | The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks |
| title_sort | fitness corrected block model or how to create maximum entropy data driven spatial social networks |
| url | https://doi.org/10.1038/s41598-022-22798-6 |
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