Related papers: Introducing Total Harmonic Resistance for Graph Ro…
Adversarial attacks on graphs have posed a major threat to the robustness of graph machine learning (GML) models. Naturally, there is an ever-escalating arms race between attackers and defenders. However, the strategies behind both sides…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
One of the intensely studied concepts of network robustness is $r$-robustness, which is a network topology property quantified by an integer $r$. It is required by mean subsequence reduced (MSR) algorithms and their variants to achieve…
Inferring a binary connectivity graph from resting-state fMRI data for a single subject requires making several methodological choices and assumptions that can significantly affect the results. In this study, we investigate the robustness…
The notions of $r$-robustness and $(r,s)$-robustness of a network have been earlier introduced in the literature to achieve resilient consensus in the presence of misbehaving agents. However, while higher robustness levels enable networks…
Spectral clustering methodologies, when extended to accommodate signed graphs, have encountered notable limitations in effectively encapsulating inherent grouping relationships. Recent findings underscore a substantial deterioration in the…
Graph-based indexes have been widely employed to accelerate approximate similarity search of high-dimensional vectors. However, the performance of graph indexes to answer different queries varies vastly, leading to an unstable quality of…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
Graph neural networks (GNNs) are the predominant architecture for learning over graphs. As with any machine learning model, an important issue is the detection of attacks, where an adversary can change the output with a small perturbation…
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
Let $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
The all-terminal reliability of a graph $G$ is the probability that $G$ remains connected when each edge fails independently with probability $p$. For fixed $n$ and $m$, the uniformly most reliable problem asks which graph with $n$ vertices…
Recognition of an adversary's objective is a core problem in physical security and cyber defense. Prior work on target recognition focuses on developing optimal inference strategies given the adversary's operating environment. However, the…
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 `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…
A total weighting of a graph $G$ is a mapping $f$ which assigns to each element $z \in V(G) \cup E(G)$ a real number $f(z)$ as its weight. The vertex sum of $v$ with respect to $f$ is $\phi_f(v)=\sum_{e \in E(v)}f(e)+f(v)$. A total…
In 1995, Brouwer proved that the toughness of a connected $k$-regular graph $G$ is at least $k/\lambda-2$, where $\lambda$ is the maximum absolute value of the non-trivial eigenvalues of $G$. Brouwer conjectured that one can improve this…
The vertex $k$-partiteness $v_k(G)$ of graph $G$ is defined as the fewest number of vertices whose deletion from $G$ yields a $k$-partite graph. In this paper, we introduce two concepts: monotonic decreasing topological index and monotonic…
Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be…