Related papers: Some Thoughts on Graph Similarity
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
Graph similarity learning refers to calculating the similarity score between two graphs, which is required in many realistic applications, such as visual tracking, graph classification, and collaborative filtering. As most of the existing…
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…
Data analysts commonly utilize statistics to summarize large datasets. While it is often sufficient to explore only the summary statistics of a dataset (e.g., min/mean/max), Anscombe's Quartet demonstrates how such statistics can be…
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different…
We study how many comparability subgraphs are needed to partition the edge set of a perfect graph. We show that many classes of perfect graphs can be partitioned into (at most) two comparability subgraphs and this holds for almost all…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to transform one graph to another. It is NP-hard to compute in general, and a…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
This article introduces a concept and measure of graph compartmentalization. This new measure allows for principled comparison between graphs of arbitrary structure, unlike existing measures such as graph modularity. The proposed measure is…
Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vessels, and filamentary structures in galaxies. To study metric…
This paper presents a spectral framework for quantifying the differentiation between graph data samples by introducing a novel metric named Graph Geodesic Distance (GGD). For two different graphs with the same number of nodes, our framework…
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…
This paper is about similarity between objects that can be represented as points in metric measure spaces. A metric measure space is a metric space that is also equipped with a measure. For example, a network with distances between its…
Based on the previously proposed concept Understanding Tree, this paper introduces two concepts: Understanding Graph and Understanding Map, and explores their potential applications. Understanding Graph and Understanding Map can be deemed…
With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of…
The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…
This paper proposes a family of graph metrics for measuring distances between graphs of different sizes. The proposed metric family defines a general form of the graph generalised optimal sub-pattern assignment (GOSPA) metric and is also…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…