Related papers: Structural Sparsity of Complex Networks: Bounded E…

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…

Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabasi-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing…

A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…

Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…

We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by…

We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…

Expansion property of a graph refers to its strong connectivity as well as sparseness. It has been reported that deep neural networks can be pruned to a high degree of sparsity while maintaining their performance. Such pruning is essential…

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…

We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their…

Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…

Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…

Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…

We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…

How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…

Network models, in which psychopathological disorders are conceptualized as a complex interplay of psychological and biological components, have become increasingly popular in the recent psychopathological literature. These network models…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…