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Signed graphs in data sciences via communicability geometry

arXiv 2403.07493 ↗First posted 12 Mar 2024math.MG cs.DM cs.LGcited by 0

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Abstract (arXiv)

Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for signed graphs and explore in depth its mathematical properties. We also prove that the communicability induces a hyperspherical geometric embedding of the signed network, and derive communicability-based metrics that satisfy the axioms of a distance even in the presence of negative edges. We then apply these metrics to solve several problems in the data analysis of signed graphs within a unified framework. These include the partitioning of signed graphs, dimensionality reduction, finding hierarchies of alliances in signed networks, and quantifying the degree of polarization between the existing factions in social systems represented by these types of graphs.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 22 of its 107 references that are in the map. First posted on arXiv 12 Mar 2024.

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22 of 107 references.

References · 22

  1. 2016Community detection in networks: A user guidecited by 105
  2. 2015Quantifying Controversy in Social Mediacited by 28
  3. 2015A Survey of Signed Network Mining in Social Mediacited by 26
  4. 2019SPONGE: A generalized eigenproblem for clustering signed networkscited by 24
  5. 2019Discovering Polarized Communities in Signed Networkscited by 20
  6. 2017Nonparametric weighted stochastic block modelscited by 10
  7. 2022Learning Stance Embeddings from Signed Social Graphscited by 8
  8. 2017On spectral partitioning of signed graphscited by 6
  9. 2022Spreading and Structural Balance on Signed Networkscited by 6
  10. 2018Balance in signed networkscited by 5
  11. 2015Stochastic block model and exploratory analysis in signed networkscited by 4
  12. 2017Balance and Frustration in Signed Networkscited by 4
10 more
  1. 2021Identifying hidden coalitions in the US House of Representatives by optimally partitioning signed networks based on generalized balancecited by 4
  2. 2020Geometry of Similarity Comparisonscited by 3
  3. 2023Introduction to correlation networks: Interdisciplinary approaches beyond thresholdingcited by 3
  4. 2014Applications of Structural Balance in Signed Social Networkscited by 2
  5. 2018Multiple Partitioning of Multiplex Signed Networks: Application to European Parliament Votescited by 2
  6. 2023Polarization and multiscale structural balance in signed networkscited by 2
  7. 2017Signed Graph Analysis for the Interpretation of Voting Behaviorcited by 1
  8. 2018Partitioning signed networkscited by 1
  9. 2021Loss of structural balance in stock marketscited by 1
  10. 2022Network bypasses sustain complexitycited by 1

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