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Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…

Recent progress has been made in understanding optimisation dynamics in neural networks trained with full-batch gradient descent with momentum with the uncovering of the edge of stability phenomenon in supervised learning. The edge of…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

The deep learning literature is continuously updated with new architectures and training techniques. However, weight initialization is overlooked by most recent research, despite some intriguing findings regarding random weights. On the…

In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…

Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis…

It is now generally assumed that the heterogeneity of most networks in nature probably arises via preferential attachment of some sort. However, the origin of various other topological features, such as degree-degree correlations and…

Eigenvector localization refers to the situation when most of the components of an eigenvector are zero or near-zero. This phenomenon has been observed on eigenvectors associated with extremal eigenvalues, and in many of those cases it can…

The ability to perform computation on devices, such as smartphones, cars, or other nodes present at the Internet of Things leads to constraints regarding bandwidth, storage, and energy, as most of these devices are mobile and operate on…

Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…

Virtual Network Embedding (VNE) approaches typically assume static or slowly-changing network topologies, but emerging applications require deployment in mobile environments where traditional methods become insufficient. This work extends…

We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…

Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…

Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the…

We design and analyze a new paradigm for building supervised learning networks, driven only by local optimization rules without relying on a global error function. Traditional neural networks with a fixed topology are made up of identical…

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…

Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…

Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features…

The changing topology of a network is driven by the need to maintain or optimize network function. As this function is often related to moving quantities such as traffic, information, etc. efficiently through the network the structure of…

Deep learning models are the most efficient models in many machine learning tasks. The main disadvantage when using them in IoT, mobile devices, independent autonomous or real-time systems is their complexity and memory size. Therefore,…