Related papers: Graphons, mergeons, and so on!
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…
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…
Graph neural networks provide a powerful toolkit for embedding real-world graphs into low-dimensional spaces according to specific tasks. Up to now, there have been several surveys on this topic. However, they usually lay emphasis on…
We develop an algorithm that finds the consensus of many different clustering solutions of a graph. We formulate the problem as a median set partitioning problem and propose a greedy optimization technique. Unlike other approaches that find…
The hierarchical graphene model is a simple toy model which is useful to understand the mechanics of renormalization group flows in super-renormalizable systems. It is based on a model of interacting electrons in graphene, for which the…
Community detection in graphs is a problem that is likely to be relevant whenever network data appears, and consequently the problem has received much attention with many different methods and algorithms applied. However, many of these…
The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks).…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Graph Neural Networks achieve state-of-the-art performance on a plethora of graph classification tasks, especially due to pooling operators, which aggregate learned node embeddings hierarchically into a final graph representation. However,…
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are…
Heterogeneous graphs are present in various domains, such as social networks, recommendation systems, and biological networks. Unlike homogeneous graphs, heterogeneous graphs consist of multiple types of nodes and edges, each representing…
Community detection is a critical challenge in analysing real graphs, including social, transportation, citation, cybersecurity, and many other networks. This article proposes three new, general, hierarchical frameworks to deal with this…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…
Graph clustering is widely used in analysis of biological networks, social networks and etc. For over a decade many graph clustering algorithms have been published, however a comprehensive and consistent performance comparison is not…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set…
We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are…