Related papers: Tensor Entropy for Uniform Hypergraphs
Let $\mathcal{H}$ be a hypergraph with $n$ vertices. Suppose that $d_1,d_2,\ldots,d_n$ are degrees of the vertices of $\mathcal{H}$. The $t$-th graph entropy based on degrees of $\mathcal{H}$ is defined as $$ I_d^t(\mathcal{H})…
While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the…
Unsupervised/self-supervised graph neural networks (GNN) are vulnerable to inherent randomness in the input graph data which greatly affects the performance of the model in downstream tasks. In this paper, we alleviate the interference of…
The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. In this work, motivated by the Shannon entropy, we propose a methodology that associates to a graph a scattering entropy, which we call…
We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy; one uses…
In recent decades, several definitions of new entropy measures have been proposed, which expands the range of applications for this important tool. The present work focuses on the extension of the classical Shannon entropy to the hyperbolic…
Here, we show a method to reconstruct connectivity hypermatrices of a general hypergraph (without any self loop or multiple edge) using tensor. We also study the different spectral properties of these hypermatrices and find that these…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…
Link prediction in graphs is studied by modeling the dyadic interactions among two nodes. The relationships can be more complex than simple dyadic interactions and could require the user to model super-dyadic associations among nodes. Such…
We introduce a novel method, called Dispersion Entropy for Graph Signals, $DE_G$, as a powerful tool for analysing the irregularity of signals defined on graphs. We demonstrate the effectiveness of $DE_G$ in detecting changes in the…
The first degree-based entropy of a graph is the Shannon entropy of its degree sequence normalized by the degree sum. In this paper, we characterize the connected graphs with given order $n$ and size $m$ that minimize the first degree-based…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
The hypergraph jump problem and the study of Lagrangians of uniform hypergraphs are two classical areas of study in the extremal graph theory. In this paper, we refine the concept of jumps to strong jumps and consider the analogous problems…
The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…