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Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…

Knowledge graph (KG) embedding methods learn geometric representations of entities and relations to predict plausible missing knowledge. These representations are typically assumed to capture rule-like inference patterns. However, our…

Knowledge Graphs (KGs) are a powerful representation of linked data, offering flexibility, semantic richness, and support for knowledge enrichment and reasoning. They help data owners organize and exploit heterogeneous data to provide…

Recently, knowledge graph (KG) augmented models have achieved noteworthy success on various commonsense reasoning tasks. However, KG edge (fact) sparsity and noisy edge extraction/generation often hinder models from obtaining useful…

Knowledge graph embedding (KGE) models learn the representation of entities and relations in knowledge graphs. Distance-based methods show promising performance on link prediction task, which predicts the result by the distance between two…

A long-standing goal in deep learning has been to characterize the learning behavior of black-box models in a more interpretable manner. For graph neural networks (GNNs), considerable advances have been made in formalizing what functions…

Graph Edit Distance (GED) is defined as the minimum cost transformation of one graph into another and is a widely adopted metric for measuring the dissimilarity between graphs. The major problem of GED is that its computation is NP-hard,…

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…

We study the problem of distance-preserving graph compression for weighted paths and trees. The problem entails a weighted graph $G = (V, E)$ with non-negative weights, and a subset of edges $E^{\prime} \subset E$ which needs to be removed…

Knowledge Graphs (KGs) represent real-world noisy raw information in a structured form, capturing relationships between entities. However, for dynamic real-world applications such as social networks, recommender systems, computational…

We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…

Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal…

The \emph{distance-number} of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the…

Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…

Answering complex questions often requires reasoning over knowledge graphs (KGs). State-of-the-art methods often utilize entities in questions to retrieve local subgraphs, which are then fed into KG encoder, e.g. graph neural networks…

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…

Representation Learning on Knowledge Graphs (KGs) is essential for downstream tasks. The dominant approach, KG Embedding (KGE), represents entities with independent vectors and faces the scalability challenge. Recent studies propose an…

Consider the continuum of points along the edges of a network, i.e., an undirected graph with positive edge weights. We measure distance between these points in terms of the shortest path distance along the network, known as the network…

While kernel methods and Graph Neural Networks offer complementary strengths, integrating the two has posed challenges in efficiency and scalability. The Graph Neural Tangent Kernel provides a theoretical bridge by interpreting GNNs through…

Knowledge Graphs (KGs), representing facts as triples, have been widely adopted in many applications. Reasoning tasks such as link prediction and rule induction are important for the development of KGs. Knowledge Graph Embeddings (KGEs)…