Social networks are often modeled by graphs, with nodes representing individuals and positively weighted edges representing the strength of the relationships between them. Working directly with such graphs is difficult, and it has become common to use spectral techniques that embed graphs in a geometry, and then work with the geometry instead. In a good embedding, edges that are heavily (positively) weighted, and so represent strong interactions, cause the vertices they connect to be embedded close to one another. However, in some social networks, there are also antagonistic relationships that are naturally represented by negatively weighted edges. The resulting graphs are called signed social networks. Clearly, an embedding of such a signed social network should place nodes connected by positively weighted edges close together, but nodes connected by negatively weighted edges far apart. Existing spectral techniques to embed signed graphs have serious drawbacks. We derive one unnormalized and two normalized spectral analysis methods for signed graphs and show, using real-world data, that they produce robust embeddings.
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Zheng, Q., Skillicorn, D.B. Modeling signed social networks using spectral embedding. Soc. Netw. Anal. Min. 11, 13 (2021). https://doi.org/10.1007/s13278-020-00718-8
- Spectral embedding
- Signed social networks
- Antagonistic relationships