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Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on…
Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds. However, most prior work assumes a purely random…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
This paper follows cognitive studies to investigate a graph representation for sketches, where the information of strokes, i.e., parts of a sketch, are encoded on vertices and information of inter-stroke on edges. The resultant graph…
A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear…
We study a well known noisy model of the graph isomorphism problem. In this model, the goal is to perfectly recover the vertex correspondence between two edge-correlated Erd\H{o}s-R\'{e}nyi random graphs, with an initial seed set of…
Graph similarity metrics serve far-ranging purposes across many domains in data science. As graph datasets grow in size, scientists need comparative tools that capture meaningful differences, yet are lightweight and scalable. Graph Relative…
Graph representation is a powerful abstraction of real-world objects and relations. Computing the Graph Edit Distance (GED) between graphs is critical in domains such as bioinformatics, machine learning, and pattern recognition. GED…
It is $\mathsf{NP}$-hard to determine the minimum number of branching vertices needed in a single-source distance-preserving subgraph of an undirected graph. We show that this problem can be solved in polynomial time if the input graph is…
We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For $\Omega \subset D = (0,1)^d$, with $d \geq 2$, we are given $n$ random i.i.d. points on $D$ whose membership in $\Omega$ is known. We…
The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations.…
Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
The graph edit distance (GED) measures the dissimilarity between two graphs as the minimal cost of a sequence of elementary operations transforming one graph into another. This measure is fundamental in many areas such as structural pattern…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…