Leaky eigenvalue problem

date: 2022-03-21


A cornerstone of the random matrix is Wigner's semi-circle law, which explains that the eigenvalues of a random matrix are bounded. This law, however, breaks if the random mtarix is extremely sparse, a problem called the leaky eigenvalue problem.

References

Range of extreme eigenvalues

Because the spectrum radius expands if d is extremely small, the modularity embedding falls short in community detection for sparse networks.