相关论文: On the geometry of exponential random graphs and a…
Low-dimensional descriptions of large systems of coupled oscillators and spiking neurons rely heavily on the Lorentzian Ansatz. We show that its privileged role is geometric rather than heuristic: for the transport induced by Riccati…
A comprehensive investigation of logN-logS distributions of gamma-ray sources discovered by EGRET has been performed for subsequent use in population studies. Existing models explaining the spatial arrangement of unidentified sources do not…
The muliplicative attribute graph (MAG) model was introduced by Kim and Leskovec as a mathematically tractable model for networks where network structure is believed to be shaped by features or attributes associated with individual nodes.…
Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions.…
We study $\gamma$-vectors associated with $h^*$-vectors of symmetric edge polytopes both from a deterministic and a probabilistic point of view. On the deterministic side, we prove nonnegativity of $\gamma_2$ for any graph and completely…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
Using our previously published algorithm, we analyze the eigenvectors of the generalized Laplacian for two metric graphs occurring in practical applications. As expected, localization of an eigenvector is rare and the network should be…
We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic $0$), which is known to admit far-reaching group-theoretic implications. We achieve complete answers to…
We consider a latent space model for random graphs where a node $i$ is associated to a random latent point $X_i$ on the Euclidean unit ball. The probability that an edge exists between two nodes is determined by a ``link'' function, which…
We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
We use a multivariate central limit theorem (CLT) to study the distribution of random geometric graphs (RGGs) on the cube and torus in the high-dimensional limit with general node distributions. We find that the distribution of RGGs on the…
Frequency power spectra due to a super-position of uncorrelated Lorentzian pulses with a random distribution of amplitudes are considered. For pulses with constant duration, there is an exponential frequency spectrum which is independent of…
The stochastic Kronecker Graph model can generate large random graph that closely resembles many real world networks. For example, the output graph has a heavy-tailed degree distribution, has a (low) diameter that effectively remains…
In this paper, we study "robust" dominating sets of random graphs that retain the domination property even if a small \emph{deterministic} set of edges are removed. We motivate our study by illustrating with examples from wireless networks…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…