Related papers: Riordan graphs I: Structural properties
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable ``interlace polynomial'' for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and…
Graph neural networks have developed by leaps and bounds in recent years due to the restriction of traditional convolutional filters on non-Euclidean structured data. Spectral graph theory mainly studies fundamental graph properties using…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the distinguished vertices. Generalizing previously known…
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
The aim of this paper is twofold. First, we demonstrate how Riordan matrices can be employed to connect well-known concepts in geometric combinatorics, such as $f$-vectors, $h$-vectors $\gamma$-vectors, in a similar fashion to the McMullen…
This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…
The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…
Graphs are fundamental mathematical structures used in various fields to represent data, signals and processes. In this paper, we propose a novel framework for learning/estimating graphs from data. The proposed framework includes (i)…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
In this paper, we introduce a novel unsupervised, graph-based filter feature selection technique which exploits the power of topologically constrained network representations. We model dependency structures among features using a family of…
The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…
Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…
We introduce orbital graphs and discuss some of their basic properties. Then we focus on their usefulness for search algorithms for permutation groups, including finding the intersection of groups and the stabilizer of sets in a group.
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…
A Riemann-Roch theorem on graph was initiated by M. Baker and S. Norine. In their article [2], a Riemann-Roch theorem on a finite graph with uniform vertex-weight and uniform edge-weight was established and it was suggested a Riemann-Roch…
We generalize the concept of token graphs to obtain supertoken graphs. In the latter case, there can be more than one token in a vertex. We formally define supertoken graphs and establish their basic properties. Moreover, we provide some…
Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows…