Related papers: Exploring complex networks via topological embeddi…
Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, the influence of the input graph's topology on GNN behavior remains poorly understood. In this work, we explore whether GNNs…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
Node embedding is the task of extracting informative and descriptive features over the nodes of a graph. The importance of node embeddings for graph analytics, as well as learning tasks such as node classification, link prediction and…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
We investigate how the topology of attributed graphs influences the distribution of node attributes. This work offers a novel perspective by treating topology and attributes as structurally distinct but interacting components. We introduce…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that…
Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological…
Network embeddings have become very popular in learning effective feature representations of networks. Motivated by the recent successes of embeddings in natural language processing, researchers have tried to find network embeddings in…
The exploitation of graph structures is the key to effectively learning representations of nodes that preserve useful information in graphs. A remarkable property of graph is that a latent hierarchical grouping of nodes exists in a global…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
For a given spatial graph $\mathcal{G} \subset \mathbb{R}^3$, we would like to find a closed orientable surface $\mathcal{S}$ embedded in $\mathbb{R}^3$ in which $\mathcal{G}$ is cellular embedded. However, for general $\mathcal{G}$ this is…
We present a local routing algorithm which guarantees delivery in all connected graphs embedded on a known surface of genus $g$. The algorithm transports $O(g\log n)$ memory and finishes in time $O(g^2n^2)$, where $n$ is the size of the…
Graph representation learning aims to effectively encode high-dimensional sparse graph-structured data into low-dimensional dense vectors, which is a fundamental task that has been widely studied in a range of fields, including machine…
Given a graph embedded in an orientable surface, a process consisting of random excitations and random node and face balancing is constructed and analyzed. It is shown that given a priori bounds g' on the genus and n' on the number of…
A signed graph (SG) is a graph where edges carry sign information attached to it. The sign of a network can be positive, negative, or neutral. A signed network is ubiquitous in a real-world network like social networks, citation networks,…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graph Neural Networks (GNNs) are powerful deep learning methods for Non-Euclidean data. Popular GNNs are message-passing algorithms (MPNNs) that aggregate and combine signals in a local graph neighborhood. However, shallow MPNNs tend to…