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We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged…
Learning parameters of latent graphical models (GM) is inherently much harder than that of no-latent ones since the latent variables make the corresponding log-likelihood non-concave. Nevertheless, expectation-maximization schemes are…
In a drawing of a clustered graph vertices and edges are drawn as points and curves, respectively, while clusters are represented by simple closed regions. A drawing of a clustered graph is c-planar if it has no edge-edge, edge-region, or…
Attribute-missing graph clustering has emerged as a significant unsupervised task, where only attribute vectors of partial nodes are available and the graph structure is intact. The related models generally follow the two-step paradigm of…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…
Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy…
This paper studies the problem of class-imbalanced graph classification, which aims at effectively classifying the graph categories in scenarios with imbalanced class distributions. While graph neural networks (GNNs) have achieved…
Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed…
Graph classification is a highly impactful task that plays a crucial role in a myriad of real-world applications such as molecular property prediction and protein function prediction.Aiming to handle the new classes with limited labeled…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…
Continual graph learning (CGL) studies the problem of learning from an infinite stream of graph data, consolidating historical knowledge, and generalizing it to the future task. At once, only current graph data are available. Although some…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
We consider the problem of learning the weighted edges of a balanced mixture of two undirected graphs from epidemic cascades. While mixture models are popular modeling tools, algorithmic development with rigorous guarantees has lagged.…
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…
Federated graph learning (FGL) has become an important research topic in response to the increasing scale and the distributed nature of graph-structured data in the real world. In FGL, a global graph is distributed across different clients,…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
Clustering a signed graph means partitioning the vertices into sets ("clusters") so that every positive edge, and no negative edge, is within a cluster. Clustering is not always possible; the obstruction is circles with exactly one negative…
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…
Signed graph clustering is a critical technique for discovering community structures in graphs that exhibit both positive and negative relationships. We have identified two significant challenges in this domain: i) existing signed spectral…