Related papers: Graphic requirements for multistationarity
In this paper, first, we establish a sufficient condition for a bipartite graph to be Hamilton-connected. Furthermore, we also give two sufficient conditions on distance signless Laplacian spectral radius for a graph to be…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…
In 1976 Frank and Gy{\'a}rf{\'a}s gave a necessary and sufficient condition for the existence of an orientation in an arbitrary graph $G$ such that for each vertex $v$, the out-degree $d^+_G(v)$ of it satisfies $p(v)\le d^+_G(v)\le q(v)$,…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…
The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its…
We consider the Cartesian product X of n finite intervals of integers and a map F from X to itself. As main result, we establish an upper bound on the number of fixed points for F which only depends on X and on the topology of the positive…
The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the…
Let $G$ be a graph with $n$ vertices, and let $A(G)$ and $D(G)$ denote respectively the adjacency matrix and the degree matrix of $G$. Define $$ A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G) $$ for any real $\alpha\in [0,1]$. The…
Generating realistic graph-structured data is challenging due to discrete connectivity, varying graph sizes, and class-specific structural patterns. Recent Generative Adversarial Networks (GAN)-based graph generation methods improve edge…
We present the methods and results of a two-stage modeling process that generates candidate gene-regulatory networks of the bacterium B. subtilis from experimentally obtained, yet mathematically underdetermined microchip array data. By…
Here we propose a generic mechanism - networked buffering - for generating robust traits in complex systems that requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role…
A recent result by Kardo\v{s}, M\'a\v{c}ajov\'a and Zerafa [J. Comb. Theory, Ser. B. 160 (2023) 1--14] related to the famous Berge-Fulkerson conjecture implies that given an arbitrary set of odd pairwise edge-disjoint cycles, say $\mathcal…
Biological systems and processes are networks of complex nonlinear regulatory interactions between nucleic acids, proteins, and metabolites. A natural way in which to represent these interaction networks is through the use of a graph. In…
We propose a partitioning of the set of unlabelled, connected cubic graphs into two disjoint subsets named genes and descendants, where the cardinality of the descendants is much larger than that of the genes. The key distinction between…
A $\mathbb{T}$-gain graph is a simple graph in which a unit complex number is assigned to each orientation of an edge, and its inverse is assigned to the opposite orientation. The associated adjacency matrix is defined canonically, and is…
This paper addresses the following question of neural network identifiability: Does the input-output map realized by a feed-forward neural network with respect to a given nonlinearity uniquely specify the network architecture, weights, and…
We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory…