Abstract
In complex real-world networks, the relation among vertices (people) changes over time. Even with millions of vertices, adding new vertices or deleting a few previous ones can drastically change the network’s dynamics. The Iterated Local Transitivity model is a deterministic model based on the principle of transitivity and local interaction among people. The same has been extended to signed social networks. Let \(\Sigma\) be a signed graph with underlying graph \(G = (V, E)\) and a function \(\sigma :E\rightarrow \{+,-\}\) assigning signs to the edges. We determine the relation between the characteristic polynomials of signed graph \(\Sigma\) and the signed graph obtained from \(\Sigma\) by adding (deleting) vertices or by adding (deleting) edges. Consequently, we present a recurrence relation for a characteristic polynomial of the Iterated Local Transitivity model for signed graphs.
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Acknowledgements
This work is supported by the Research Grant from the University Grants Commission [NTA Ref. No.: 211610017285] for the third author.
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Rao, A.K., Kaur, B., Somra, S. et al. Spectral analysis for signed social networks. AAECC (2023). https://doi.org/10.1007/s00200-023-00639-x
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DOI: https://doi.org/10.1007/s00200-023-00639-x