相关论文: Lecture Notes on Evasiveness of Graph Properties

Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…

In this note, we show that three graph properties - strong connectivity, acyclicity, and reachability from a vertex $s$ to all vertices - each require a working memory of $\Omega (\epsilon m)$ on a graph with $m$ edges to be determined…

We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as…

In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…

A key concept for many graph layout algorithms is planarity, a graph property that allows to draw vertices and edges crossing-free in the plane. Important is the generalization to $k$-planar graphs, which can be drawn in the plane with at…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems…

The first author together with Jenssen, Perkins and Roberts (2017) recently showed how local properties of the hard-core model on triangle-free graphs guarantee the existence of large independent sets, of size matching the best-known…

Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property.…

We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…

Graph Neural Networks (GNNs) have achieved promising results in tasks such as node classification and graph classification. However, recent studies reveal that GNNs are vulnerable to backdoor attacks, posing a significant threat to their…

Graph auto-encoders have proved to be useful in network embedding task. However, current models only consider explicit structures and fail to explore the informative latent structures cohered in networks. To address this issue, we propose a…

This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…

We live in a world increasingly dominated by networks -- communications, social, information, biological etc. A central attribute of many of these networks is that they are dynamic, that is, they exhibit structural changes over time. While…

Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…

We consider the problem of recovering a latent graph where the observations at each node are \emph{aliased}, and transitions are stochastic. Observations are gathered by an agent traversing the graph. Aliasing means that multiple nodes emit…

In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that…

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…

Graph representation learning, a critical step in graph-centric tasks, has seen significant advancements. Earlier techniques often operate in an end-to-end setting, which heavily rely on the availability of ample labeled data. This…