相关论文: Algorithmic Decorrelation and Planted Clique in De…
Finding densely connected groups of nodes in networks is a widely used tool for analysis in graph mining. A popular choice for finding such groups is to find subgraphs with a high average degree. While useful, interpreting such subgraphs…
We prove that if $p\ge n^{-\frac{1}{3}+\beta}$ for some $\beta > 0$, then asymptotically almost surely the binomial random graph $G(n,p)$ has a $K_3$-packing containing all but at most $n + O(1)$ edges. Similarly, we prove that if $d \ge…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
The node-averaged complexity of a distributed algorithm running on a graph $G=(V,E)$ is the average over the times at which the nodes $V$ of $G$ finish their computation and commit to their outputs. We study the node-averaged complexity for…
Graph anomaly detection (GAD) is widely applied in many areas, such as financial fraud detection and social spammer detection. Anomalous nodes in the graph not only impact their own communities but also create a ripple effect on neighbors…
Given connected graph $H$ which is not a star, we show that the number of copies of $H$ in a dense uniformly random regular graph is asymptotically Gaussian, which was not known even for $H$ being a triangle. This addresses a question of…
A \emph{locally irregular graph} is a graph whose adjacent vertices have distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally irregular subgraphs if its edge set may be partitioned into $k$ subsets each of which…
In the noisy channel model from coding theory, we wish to detect errors introduced during transmission by optimizing various parameters of the code. Bennett, Dudek, and LaForge framed a variation of this problem in the language of…
The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a…
Graph Neural Networks (GNNs) have achieved promising results for semi-supervised learning tasks on graphs such as node classification. Despite the great success of GNNs, many real-world graphs are often sparsely and noisily labeled, which…
Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…
Let G = (V,E) be an n-vertex graph and M_d a d-vertex graph, for some constant d. Is M_d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log…
High triangle density -- the graph property stating that a constant fraction of two-hop paths belong to a triangle -- is a common signature of social networks. This paper studies triangle-dense graphs from a structural perspective. We prove…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
We give a polynomial-time algorithm that finds a planted clique of size $k \ge \sqrt{n \log n}$ in the semirandom model, improving the state-of-the-art $\sqrt{n} (\log n)^2$ bound. This $\textit{semirandom planted clique problem}$ concerns…
The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an…
Graph signal processing (GSP) is a key tool for satisfying the growing demand for information processing over networks. However, the success of GSP in downstream learning and inference tasks is heavily dependent on the prior identification…
To understand how hidden information can be extracted from statistical networks, planted models in random graphs have been the focus of intensive study in recent years. In this work, we consider the detection of a planted matching, i.e., an…
In this paper, we study the problem of detecting the presence of a planted perfect matching or spanning tree in an Erd\H{o}s--R\'enyi random graph. More precisely, we study the hypothesis testing problem where the statistician observes a…
The correlated Erd\"os-R\'enyi random graph ensemble is a probability law on pairs of graphs with $n$ vertices, parametrized by their average degree $\lambda$ and their correlation coefficient $s$. It can be used as a benchmark for the…