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Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…

In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…

A challenge in transmission-distribution coordination is how to quickly and reliably coordinate Distributed Energy Resources (DERs) across large multi-stakeholder Distribution Networks (DNs) to support the Transmission Network (TN), while…

The success of deep learning ignited interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural…

Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…

Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…

In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…

We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly…

Hierarchically modular organization is a canonical network topology that is evolutionarily conserved in the nervous systems of animals. Within the network, neurons form directional connections defined by the growth of their axonal…

Understanding how different networks relate to each other is key for obtaining a greater insight into complex systems. Here, we introduce an intuitive yet powerful framework to characterise the relationship between two networks comprising…

The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from…

Many biological, technological, and social systems can be effectively described as networks of interacting subsystems. Typically, these networks are not isolated objects, but interact with their environment through both signals and…

This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…

The voter model with the node update rule is numerically investigated on a directed network. We start from a directed hierarchical tree, and split and rewire each incoming arc at the probability $p$. In order to discriminate the better and…

A feedback neural network approach to communication routing problems is developed with emphasis on Multiple Shortest Path problems, with several requests for transmissions between distinct start- and endnodes. The basic ingredients are a…

Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…

In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical…

Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to…

Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward…