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Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two…

In discrete choice experiments, the information matrix depends on the model parameters. Therefore designing optimally informative experiments for arbitrary initial parameters often yields highly nonlinear optimization problems and makes…

Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…

Directed networks are essential for representing complex systems, capturing the asymmetry of interactions in fields such as neuroscience, transportation, and social networks. Directionality reveals how influence, information, or resources…

Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian…

We consider the minimum-cut partitioning of a graph into more than two parts using spectral methods. While there exist well-established spectral algorithms for this problem that give good results, they have traditionally not been well…

Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial…

We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…

Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…

We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graphs is used to characterize directed acyclic graphs. Moreover,…

A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…

Unified understanding of neuro networks (NNs) gets the users into great trouble because they have been puzzled by what kind of rules should be obeyed to optimize the internal structure of NNs. Considering the potential capability of random…

Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…

Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…

We propose an algorithm to locate the most critical nodes to network robustness. Such critical nodes may be thought of as those most related to the notion of network centrality. Our proposal relies only on a localized spectral analysis of a…

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the…