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In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
A distance graph is an undirected graph on the integers where two integers are adjacent if their difference is in a prescribed distance set. The independence ratio of a distance graph $G$ is the maximum density of an independent set in $G$.…
Digital presence in the world of online social media entails significant privacy risks. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the…
The minimum distance of a code is an important concept in information theory. Hence, computing the minimum distance of a code with a minimum computational cost is a crucial process to many problems in this area. In this paper, we present…
We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and…
In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…
It is known that electrical networks with resistors are related to the Laplace operator and random walk on weighted graphs. In this paper we consider more general electrical networks with coils, capacitors, and resistors. We give two…
A strongly connected digraph is called a cactoid-type if each of its blocks is a digraph consisting of finitely many oriented cycles sharing a common directed path. In this article, we find the formula for the determinant of the distance…
Given an undirected graph, the resistance distance between two nodes is the resistance one would measure between these two nodes in an electrical network if edges were resistors. Summing these distances over all pairs of nodes yields the…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world…
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…
Graph edit distance (GED) is a powerful and flexible graph matching paradigm that can be used to address different tasks in structural pattern recognition, machine learning, and data mining. In this paper, some new binary linear programming…
A graph $G$ is called a cactus if each block of $G$ is either an edge or a cycle. Denote by $Cact(n;t)$ the set of connected cacti possessing $n$ vertices and $t$ cycles. In this paper, we show that there are some errors in [J. Du, G. Su,…
We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterization of the solutions is obtained in the case when the…
We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various…