Related papers: Graphic requirements for multistationarity
Statistical inference of genetic regulatory networks is essential for understanding temporal interactions of regulatory elements inside the cells. For inferences of large networks, identification of network structure is typical achieved…
Z-mapping graph is a balanced bipartite graph $G$ of a digraph $D$ by split each vertex of $D$ into a pair of vertices of $G$. Based on the property of the $G$, it is proved that if $D$ is strong connected and $G$ is Hamiltonian, then $D$…
We present a graphical criterion for reading dependencies from the minimal directed independence map G of a graphoid p when G is a polytree and p satisfies composition and weak transitivity. We prove that the criterion is sound and…
We examine the generic local and global rigidity of various graphs in R^d. Bruce Hendrickson showed that some necessary conditions for generic global rigidity are (d+1)-connectedness and generic redundant rigidity and hypothesized that they…
The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world…
Let $G$ be a graph. We denote by $e(G)$ and $\rho(G)$ the size and the spectral radius of $G$. A spanning subgraph $F$ of $G$ is called an even factor of $G$ if $d_F(v)\in\{2,4,6,\ldots\}$ for every $v\in V(G)$. Yan and Kano provided a…
A key feature of neural network architectures is their ability to support the simultaneous interaction among large numbers of units in the learning and processing of representations. However, how the richness of such interactions trades off…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing…
In data transmission networks, the availability of data transmission is equivalent to the existence of the fractional factor of the corresponding graph which is generated by the network. Research on the existence of fractional factors under…
For a given graph \( G \), let \( A(G) \), \( Q(G) \), and \( D(G) \) denote the adjacency matrix, signless Laplacian matrix, and diagonal degree matrix of \( G \), respectively. The \( A_\alpha(G) \) matrix, proposed by Nikiforov, is…
We study the onset of spatial instabilities in reaction networks where the spatially homogeneous system admits a steady state parameterization. We formulate a sufficient condition -- based on the signs of the constant and leading…
Motivated by problems modeling the spread of infections in networks, in this paper we explore which bipartite graphs are most resilient to widespread infections under various parameter settings. Namely, we study bipartite networks with a…
Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. Population structures can be expressed as configurations. Such configurations…
Assume that $G$ is a finite group and let $a$ and $b$ be non-negative integers. We define an undirected graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and…
We conduct a series of experiments designed to empirically demonstrate the effects of varying the structural features of a multi-agent emergent communication game framework. Specifically, we model the interactions (edges) between individual…
The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The…
Graph neural networks (GNNs) have achieved remarkable success in processing graph-structured data across various applications. A critical aspect of real-world graphs is their dynamic nature, where new nodes are continually added and…
A \emph{uniform random intersection graph} $G(n,m,k)$ is a random graph constructed as follows. Label each of $n$ nodes by a randomly chosen set of $k$ distinct colours taken from some finite set of possible colours of size $m$. Nodes are…
We present determinant criteria for the preclusion of non-degenerate multiple steady states in networks of interacting species. A network is modeled as a system of ordinary differential equations in which the form of the species formation…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…