124 citations · 280 across the 33 of their papers we have counts for
34 papers
Cheeger-type inequalities for the second largest spectral gap from of the normalized Laplacian
Lies Beers, Raffaella Mulas, Jan Petr
We study the second largest spectral gap from of the normalized Laplacian of a graph, a quantity that appears in the literature in connection with random walks, expander graphs…
Spectral Perspectives on FAT Graph Colorings
Lies Beers, Raffaella Mulas
We investigate Fair and Tolerant (FAT) graph colorings, a coloring framework in which each vertex is allowed to share its color with a prescribed fraction of its neighbors, while t…
Fair and Tolerant (FAT) Graph Colorings
Lies Beers, Raffaella Mulas
We introduce and study Fair and Tolerant colorings (FAT colorings), where each vertex tolerates a given fraction of same-colored neighbors while fairness is preserved across the ot…
Coloring outside the lines: Spectral bounds for generalized hypergraph colorings
Lies Beers, Raffaella Mulas
It is known that, for an oriented hypergraph with (vertex) coloring number and smallest and largest normalized Laplacian eigenvalues and , respectively, the inequali…
At the end of the spectrum: Chromatic bounds for the largest eigenvalue of the normalized Laplacian
Lies Beers, Raffaella Mulas
For a graph with largest normalized Laplacian eigenvalue and (vertex) coloring number , it is known that . Here we prove properties of graphs for which th…
Maximal colourings for graphs
Raffaella Mulas
We consider two different notions of graph colouring, namely, the -periodic colouring for vertices that has been introduced in 1974 by Bondy and Simonovits, and the periodic col…
Uniform density in matroids, matrices and graphs
Karel Devriendt, Raffaella Mulas
We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a…
There is no going back: Properties of the non-backtracking Laplacian
Raffaella Mulas, Dong Zhang, Giulio Zucal
We prove new properties of the non-backtracking graph and the non-backtracking Laplacian for graphs. In particular, among other results, we prove that two simple graphs are isomorp…
A measure-theoretic representation of graphs
Raffaella Mulas, Giulio Zucal
Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to define a new notion of pseudo-metr…
On Turán numbers for disconnected hypergraphs
Raffaella Mulas, Jiaxi Nie
We introduce the following simpler variant of the Turán problem: Given integers and , what is the smallest integer for which there exists an -uniform…
Spectral theory of the non-backtracking Laplacian for graphs
Jürgen Jost, Raffaella Mulas, Leo Torres
We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that…
Petals and Books: The largest Laplacian spectral gap from 1
Jürgen Jost, Raffaella Mulas, Dong Zhang
We prove that, for any connected graph on vertices, the spectral gap from the value with respect to the normalized Laplacian is at most . Moreover, we show that…
Random walks and Laplacians on hypergraphs: When do they match?
Raffaella Mulas, Christian Kuehn, Tobias Böhle +1
We develop a general theory of random walks on hypergraphs which includes, as special cases, the different models that are found in literature. In particular, we introduce and anal…
Interlacing Results for Hypergraphs
Raffaella Mulas
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their…
Estimating cellular redundancy in networks of genetic expression
Raffaella Mulas, Michael J. Casey
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the mu…
Spectral theory of weighted hypergraphs via tensors
Francesco Galuppi, Raffaella Mulas, Lorenzo Venturello
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this…
Coupled Hypergraph Maps and Chaotic Cluster Synchronization
Tobias Böhle, Christian Kuehn, Raffaella Mulas +1
Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and non…
Spectra of Complex Unit Hypergraphs
Raffaella Mulas, Nathan Reff
A complex unit hypergraph is a hypergraph where each vertex-edge incidence is given a complex unit label. We define the adjacency, incidence, Kirchoff Laplacian and normalized Lapl…
A Cheeger Cut for Uniform Hypergraphs
Raffaella Mulas
The graph Cheeger constant and Cheeger inequalities are generalized to the case of hypergraphs whose edges have the same cardinality. In particular, it is shown that the second lar…
Normalized Laplace Operators for Hypergraphs with Real Coefficients
Jürgen Jost, Raffaella Mulas
Chemical hypergraphs and their associated normalized Laplace operators are generalized and studied in the case where each vertex--hyperedge incidence has a real coefficient. We sys…
Geometry and symmetry in biochemical reaction systems
Raffaella Mulas, Rubén J. Sánchez-García, Ben D. MacArthur
Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the…
Coloring the normalized Laplacian for oriented hypergraphs
Aida Abiad, Raffaella Mulas, Dong Zhang
The independence number, coloring number and related parameters are investigated in the setting of oriented hypergraphs using the spectrum of the normalized Laplace operator. For t…
Spectral classes of hypergraphs
Raffaella Mulas
The notions of spectral measures and spectral classes, which are well known for graphs, are generalized and investigated for oriented hypergraphs.
-Laplace Operators for Oriented Hypergraphs
Jürgen Jost, Raffaella Mulas, Dong Zhang
The -Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particu…