Related papers: A Perron-Frobenius theory for block matrices assoc…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes…
We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare…
The hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the Cartesian product. Here we study the eigenvalue spectrum…
Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
We prove some eigenvalue inequalities for positive semidefinite matrices partitioned into four blocks. The inradius of the numerical range of the off-diagonal block contributes to these estimates. Some related norm inequalities are given…
The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
We propose a novel numerical method for solving a quadratic vector equation arising in Markovian Binary Trees. The numerical method consists in a fixed point iteration, expressed by means of the Perron vectors of a sequence of nonnegative…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
The Frobenius-Perron theory of an endofunctor of a $\Bbbk$-linear category (recently introduced in [CG]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories…
Information of localization properties of eigenvectors of the complex network has applicability in many different areas which include networks centrality measures, spectral partitioning, development of approximation algorithms, and disease…
This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector, which directly leads to max analogues of some classical results for complex matrices. We also…
A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The…
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
In this paper, we consider convergence properties of a second order Markov chain. Similar to a column stochastic matrix is associated to a Markov chain, a so called {\em transition probability tensor} $P$ of order 3 and dimension $n$ is…