Related papers: On anti-stochastic properties of unlabeled graphs
Let the class A of graphs be bridge-addable; that is, whenever a graph G in A has vertices u and v in different components then the graph G+uv is in A. For a random graph sampled uniformly from the graphs in A on vertex set {1,..,n}, there…
The area of graph property testing seeks to understand the relation between the global properties of a graph and its local statistics. In the classical model, the local statistics of a graph is defined relative to a uniform distribution…
This paper has dual aims. First is to develop practical universal coding methods for unlabeled graphs. Second is to use these for graph anomaly detection. The paper develops two coding methods for unlabeled graphs: one based on the degree…
An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…
The Graph Reconstruction Conjecture famously posits that any undirected graph on at least three vertices is determined up to isomorphism by its family of (unlabeled) induced subgraphs. At present, the conjecture admits partial resolutions…
Graph classification has practical applications in diverse fields. Recent studies show that graph-based machine learning models are especially vulnerable to adversarial perturbations due to the non i.i.d nature of graph data. By adding or…
Graph contrastive learning is the state-of-the-art unsupervised graph representation learning framework and has shown comparable performance with supervised approaches. However, evaluating whether the graph contrastive learning is robust to…
The shift-enabled property of an underlying graph is essential in designing distributed filters. This article discusses when a random graph is shift-enabled. In particular, popular graph models ER, WS, BA random graph are used, weighted and…
Graph Neural Networks (GNNs) have shown remarkable performance on graph-structured data. However, recent empirical studies suggest that GNNs are very susceptible to distribution shift. There is still significant ambiguity about why…
A graph-based sampling and consensus (GraphSAC) approach is introduced to effectively detect anomalous nodes in large-scale graphs. Existing approaches rely on connectivity and attributes of all nodes to assign an anomaly score per node.…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…
The increased use of cryptography to protect our personal information makes us want to understand the security of cryptosystems. The security of many cryptosystems relies on solving the discrete logarithm, which is thought to be relatively…
We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…
One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability…
We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the…
We enumerate factorisations of the complete bipartite graph into spanning semiregular graphs in several cases, including when the degrees of all the factors except one or two are small. The resulting asymptotic behaviour is seen to…
Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the…