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Graph deep learning models, such as graph convolutional networks (GCN) achieve remarkable performance for tasks on graph data. Similar to other types of deep models, graph deep learning models often suffer from adversarial attacks. However,…
Recently, there has been great success in applying deep neural networks on graph structured data. Most work, however, focuses on either node- or graph-level supervised learning, such as node, link or graph classification or node-level…
The goal of graph inference is to design algorithms for learning properties of a hidden graph using queries to an oracle that returns information about the graph. Graph reconstruction, verification, and property testing are all types of…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
For any fixed positive integer $r$ and a given budget $k$, the $r$-\textsc{Eigenvalue Vertex Deletion} ($r$-EVD) problem asks if a graph $G$ admits a subset $S$ of at most $k$ vertices such that the adjacency matrix of $G\setminus S$ has at…
Deep learning on graph structures has shown exciting results in various applications. However, few attentions have been paid to the robustness of such models, in contrast to numerous research work for image or text adversarial attack and…
One of the most significant challenges in combating against the spread of infectious diseases was the difficulty in estimating the true magnitude of infections. Unreported infections could drive up disease spread, making it very hard to…
Estimating individual treatment effect (ITE) from observational graph data is crucial for decision-making in the fields such as commerce and medicine. This task is challenging due to interference, where individual outcomes can be influenced…
A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$…
For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygon) associated with the first (non-trivial) eigenvalue. In…
Low-dimension graph embeddings have proved extremely useful in various downstream tasks in large graphs, e.g., link-related content recommendation and node classification tasks, etc. Most existing embedding approaches take nodes as the…
We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…
Let $G$ be a finite undirected graph with edge set $E$. An edge set $E' \subseteq E$ is an {\em induced matching} in $G$ if the pairwise distance of the edges of $E'$ in $G$ is at least two; $E'$ is {\em dominating} in $G$ if every edge $e…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
Complex networks or graphs provide a powerful framework to understand importance of individuals and their interactions in real-world complex systems. Several graph theoretical measures have been introduced to access importance of the…
With the shift towards decentralized energy generation, the increasing complexity of power systems renders physics-based modeling challenging. At the same time the growing amount of available measurement data opens the door for obtaining…
Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to…
Given a time series of graphs G(t) = (V, E(t)), t = 1, 2, ..., where the fixed vertex set V represents "actors" and an edge between vertex u and vertex v at time t (uv \in E(t)) represents the existence of a communications event between…
This is the first in a series of six articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. Many of…
Deep graph embedding is an important approach for community discovery. Deep graph neural network with self-supervised mechanism can obtain the low-dimensional embedding vectors of nodes from unlabeled and unstructured graph data. The…