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Due to the ever rising importance of the network paradigm across several areas of science, comparing and classifying graphs represent essential steps in the networks analysis of complex systems. Both tasks have been recently tackled via…
The biharmonic distance is a fundamental metric on graphs that measures the dissimilarity between two nodes, capturing both local and global structures. It has found applications across various fields, including network centrality, graph…
Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…
Many tasks that rely on representations of nodes in graphs would benefit if those representations were faithful to distances between nodes in the graph. Geometric techniques to extract such representations have poor scaling over large graph…
The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…
In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
Existing performance measures rank delineation algorithms inconsistently, which makes it difficult to decide which one is best in any given situation. We show that these inconsistencies stem from design flaws that make the metrics…
Urban region profiling can benefit urban analytics. Although existing studies have made great efforts to learn urban region representation from multi-source urban data, there are still three limitations: (1) Most related methods focused…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G\subsetneq\mathbb{R}^n$ by using the arithmetic or the logarithmic mean of the Euclidean distances from the points $x$ and $y$ to the…
Random geometric graphs are random graph models defined on metric measure spaces. A random geometric graph is generated by first sampling points from a metric space and then connecting each pair of sampled points independently with a…
The issue of bias (i.e., systematic unfairness) in machine learning models has recently attracted the attention of both researchers and practitioners. For the graph mining community in particular, an important goal toward algorithmic…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Color maps are a commonly used visualization technique in which data are mapped to optical properties, e.g., color or opacity. Color maps, however, do not explicitly convey structures (e.g., positions and scale of features) within data.…
One of the main reasons for topological persistence being useful in data analysis is that it is backed up by a stability (isometry) property: persistence diagrams of $1$-parameter persistence modules are stable in the sense that the…
To investigate the topological structure of planar polygon decomposition on trapezoids, which is formed by height functions. We use the oriented Reeb graph of the function with a marked vertex. We describe all possible optimal Reeb graphs…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…