Marianna Bolla

Learn More
Two penalized-balanced and normalized-versions of the Newman-Girvan modularity are introduced and estimated by the non-negative eigenvalues of the modularity and normalized modularity matrix, respectively. In this way, the partition of the vertices that maximizes the modularity can be obtained by applying the k-means algorithm for the representatives of the(More)
Bolla, M., Spectra, Euclidean representations and clusterings of hypergraphs, Discrete Mathematics 117 (1993) 19-39. We would like to classify the vertices of a hypergraph in the way that ‘similar’ vertices (those having many incident edges in common) belong to the same cluster. The problem is formulated as follows: given a connected hypergraph on n(More)
Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to Wigner-noise is investigated. It is proved that such an m×n matrix almost surely has a constant number of large singular values (of order √ mn), while the rest of the singular values are of order √ m + n as m,n → ∞.(More)
Testable weighted graph parameters and equivalent notions of testability – proved in [4] for simple graphs – are generalized for vertexand edge-weighted graphs with no dominant vertex-weights. We prove that certain balanced minimum multiway cut densities are testable. Using this fact, quadratic programming techniques are applied to approximate some of these(More)
Spectra and representations of some special weighted graphs are investigated with weight matrices consisting of homogeneous blocks. It is proved that a random perturbation of the weight matrix or that of the weighted Laplacian with a “Wignernoise” will not have an effect on the order of the protruding eigenvalues and the representatives of the vertices will(More)
The minimum k-way discrepancy mdk(C) of a rectangular matrix C of nonnegative entries is the minimum of the maxima of the withinand between-cluster discrepancies that can be obtained by simultaneous k-clusterings (proper partitions) of its rows and columns. In Theorem 2, irrespective of the size of C, we give the following estimate for the kth largest(More)
Factors, obtained by correspondence analysis, are used to find biclustering of a contingency table such that the row–column cluster pairs are regular, i.e., they have small discrepancy. In our main theorem, the constant of the so-called volumeregularity is related to the SVD of the normalized contingency table. This result is applicable to two-way cuts when(More)
Expander graphs are widely used in communication problems and construction of error correcting codes. In such graphs, information gets through very quickly. Typically, it is not true for social or biological networks, though we may find a partition of the vertices such that the induced subgraphs on them and the bipartite subgraphs between any pair of them(More)