L. Sibemberg

collaborators

5 papers

cs.SI2026

Spectral graph clustering with inhomogeneous latent geometry

Konstantin Avrachenkov, Lucas S. Sibemberg, Alexander Van Werde

We study spectral clustering in the presence of a confounding latent geometry. The leading eigenvectors may then be dominated by the latent geometry rather than by the communities.…

math.CO2026

On the minimum number of eigenvalues of matrices associated with cographs

Luiz Emilio Allem, Martin FÃ¼rer, Carlos Hoppen +2

A symmetric matrix $M = (m_{ij}) \in R^{n \times n}$ is said to be associated with an $n$ -vertex graph $G = (V, E)$ with vertex set ${v_{1}, \dots, v_{n}}$ if, for every $i \neq j…

cs.SI2025

Multi-Community Spectral Clustering for Geometric Graphs

Luiz Emilio Allem, Konstantin Avrachenkov, Carlos Hoppen +2

In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clusteri…

math.CO2025

The minimum number of distinct eigenvalues of a threshold graph is at most $4$

Luiz Emilio Allem, Carlos Hoppen, JoÃ£o Lazzarin +2

In this note we show that the minimum number of distinct eigenvalues of a threshold graph is at most $4$ . Moreover, given any threshold graph $G$ and any nonzero real number $I^»$ ,…

math.CO2025

On the minimum number of eigenvalues of trees of diameter seven

Luiz Emilio Allem, Carlos Hoppen, Lucas Siviero Sibemberg

The underlying graph $G$ of a symmetric matrix $M = (m_{ij}) \in R^{n \times n}$ is the graph with vertex set ${v_{1}, \dots, v_{n}}$ such that a pair ${v_{i}, v_{j}}$ with $i\neq j…