Corpus ID: 117948341

When the largest eigenvalue of the modularity and normalized modularity matrix is zero

  title={When the largest eigenvalue of the modularity and normalized modularity matrix is zero},
  author={Marianna Bolla and Brian Bullins and Sorathan Chaturapruek and Shiwen Chen and Katalin Friedl},
  journal={arXiv: Spectral Theory},
In July 2012, at the Conference on Applications of Graph Spectra in Computer Science, Barcelona, D. Stevanovic posed the following open problem: which graphs have the zero as the largest eigenvalue of their modularity matrix? The conjecture was that only the complete and complete multipartite graphs. They indeed have this property, but are they the only ones? In this paper, we will give an affirmative answer to this question and prove a bit more: both the modularity and the normalized… Expand
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