Related papers: Aspects of randomness in neural graph structures
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Knowledge graphs play a central role for linking different data which leads to multiple layers. Thus, they are widely used in big data integration, especially for connecting data from different domains. Few studies have investigated the…
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…
Network science provides valuable insights across numerous disciplines including sociology, biology, neuroscience and engineering. A task of major practical importance in these application domains is inferring the network structure from…
Deep neural networks for graphs have emerged as a powerful tool for learning on complex non-euclidean data, which is becoming increasingly common for a variety of different applications. Yet, although their potential has been widely…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
Many real world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
Signal processing on graphs has received a lot of attention in the recent years. A lot of techniques have arised, inspired by classical signal processing ones, to allow studying signals on any kind of graph. A common aspect of these…
We develop a new class of random graph models for the statistical estimation of network formation -- subgraph generated models (SUGMs). Various subgraphs -- e.g., links, triangles, cliques, stars -- are generated and their union results in…
Sampling is an established technique to scale graph neural networks to large graphs. Current approaches however assume the graphs to be homogeneous in terms of relations and ignore relation types, critically important in biomedical graphs.…
The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain.…
Understanding how neural networks generalize on unseen data is crucial for designing more robust and reliable models. In this paper, we study the generalization gap of neural networks using methods from topological data analysis. For this…
The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying…
Intrinsic brain activity is characterized by highly structured co-activations between different regions, whose origin is still under debate. In this paper, we address the question whether it is possible to unveil how the underlying…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…