Related papers: Graph Similarity and Homomorphism Densities
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
Similarity measures are used extensively in machine learning and data science algorithms. The newly proposed graph Relative Hausdorff (RH) distance is a lightweight yet nuanced similarity measure for quantifying the closeness of two graphs.…
For graphs $G$ and $H$, a \emph{homomorphism} from $G$ to $H$ is an edge-preserving mapping from the vertex set of $G$ to the vertex set of $H$. For a fixed graph $H$, by \textsc{Hom($H$)} we denote the computational problem which asks…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation…
Two graphs $G$ and $H$ are homomorphism indistinguishable over a graph class $\mathcal{F}$ if they admit the same number of homomorphisms from every graph $F \in \mathcal{F}$. Many graph isomorphism relaxations such as (quantum) isomorphism…
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and bioinformatics, among others. Discovery and…
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…
The notion of $\mathcal{H}$-treewidth, where $\mathcal{H}$ is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of $\mathcal{H}$-treewidth at most $k$…
For a vertex set $S\subseteq V(G)$ in a graph $G$, the {\em distance multiset}, $D(S)$, is the multiset of pairwise distances between vertices of $S$ in $G$. Two vertex sets are called {\em homometric} if their distance multisets are…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
For a graph $G=(V,E)$ and positive integer $p$, the exact distance-$p$ graph $G^{[\natural p]}$ is the graph with vertex set $V$ and with an edge between vertices $x$ and $y$ if and only if $x$ and $y$ have distance $p$. Recently, there has…
In this paper, we study Gromov hyperbolicity and related parameters, that represent how close (locally) a metric space is to a tree from a metric point of view. The study of Gromov hyperbolicity for geodesic metric spaces can be reduced to…
Recently, the theory of dense graph limits has received attention from multiple disciplines including graph theory, computer science, statistical physics, probability, statistics, and group theory. In this paper we initiate the study of the…
Understanding generalization and robustness of machine learning models fundamentally relies on assuming an appropriate metric on the data space. Identifying such a metric is particularly challenging for non-Euclidean data such as graphs.…
There are several notions of convergence for sequences of bounded degree graphs. One such notion is left convergence, which is based on counting neighborhood distributions. Another notion is right convergence, based on counting…
We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and…
Graph homomorphism has been an important research topic since its introduction [17]. Stated in the language of binary relational structures in that paper [17], Lov\'asz proved a fundamental theorem that, for a graph $H$ given by its $0$-$1$…
Given a graph G, we investigate the question of determining the parity of the number of homomorphisms from G to some other fixed graph H. We conjecture that this problem exhibits a complexity dichotomy, such that all parity graph…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…