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Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the…
Graph Convolutional Networks (GCNs) are specialized neural networks for feature extraction from graph-structured data. In contrast to traditional convolutional networks, GCNs offer distinct advantages when processing irregular data, which…
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…
We consider spectral methods that uncover hidden structures in directed networks. We establish and exploit connections between node reordering via (a) minimizing an objective function and (b) maximizing the likelihood of a random graph…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of…
Graph kernels are usually defined in terms of simpler kernels over local substructures of the original graphs. Different kernels consider different types of substructures. However, in some cases they have similar predictive performances,…
Networks arise in many applications, such as in the analysis of text documents, social interactions and brain activity. We develop a general framework for extrinsic statistical analysis of samples of networks, motivated by networks…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
We propose a method for demonstrating sub community structure in scientific networks of relatively small size from analyzing databases of publications. Research relationships between the network members can be visualized as a graph with…
We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph…
We propose a quantum algorithm for calculating the structural properties of complex networks and graphs. The corresponding protocol -- deteQt -- is designed to perform large-scale community and botnet detection, where a specific subgraph of…
The spectral graph theory provides an algebraical approach to investigate the characteristics of weighted networks using the eigenvalues and eigenvectors of a matrix (e.g., normalized Laplacian matrix) that represents the structure of the…
Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
The representation of a biochemical network as a graph is the coarsest level of description in cellular biochemistry. By studying the network structure one can draw conclusions on the large scale organisation of the biochemical processes.…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
We show that a network can self-organize its structure in a completely distributed manner in order to optimize its synchronizability whilst satisfying the local constraints: non-negativity of edge weights, and maximum weighted degree of…
Big graph mining is an important research area and it has attracted considerable attention. It allows to process, analyze, and extract meaningful information from large amounts of graph data. Big graph mining has been highly motivated not…
The notion of barycentre graph is of crucial importance for machine learning algorithms that process graph-valued data. The barycentre graph is a "summary graph" that captures the mean topology and connectivity structure of a training…