Related papers: Dynamical importance and network perturbations
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
Random graphs are useful tools to study social interactions. In particular, the use of weighted random graphs allows to handle a high level of information concerning which agents interact and in which degree the interactions take place.…
Community structure analysis is a powerful tool for complex networks, which can simplify their functional analysis considerably. Recently, many approaches were proposed to community structure detection, but few works were focused on the…
Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
Synchronization in dynamical systems on directed weighted networks is often associated with stronger coupling and denser interactions. This paper shows that the opposite can also occur: weakening selected edges may increase the generalized…
We describe centralities in temporal networks using a supracentrality framework to study centrality trajectories, which characterize how the importances of nodes change in time. We study supracentrality generalizations of eigenvector-based…
In graph analyses, directed edges are often approximated to undirected ones so that the adjacency matrices may be symmetric. However, such simplification has not been thoroughly verified. In this study, we investigate how directedness…
One practice of employing deep neural networks is to apply the same architecture to all the input instances. However, a fixed architecture may not be representative enough for data with high diversity. To promote the model capacity,…
We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should…
This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is…
Identifying the most influential nodes in information networks has been the focus of many research studies. This problem has crucial applications in various contexts, such as controlling the propagation of viruses or rumours in real-world…
We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many…
Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of…
We introduce a new dynamic data structure for maintaining the strongly connected components (SCCs) of a directed graph (digraph) under edge deletions, so as to answer a rich repertoire of connectivity queries. Our main technical…
Networks significantly influence social, economic, and organizational outcomes, with centrality measures serving as crucial tools to capture the importance of individual nodes. This paper introduces Laplacian Eigenvector Centrality (LEC), a…
The principal ratio of a connected graph $G$, $\gamma(G)$, is the ratio between the largest and smallest coordinates of the principal eigenvector of the adjacency matrix of $G$. Over all connected graphs on $n$ vertices, $\gamma(G)$ ranges…
We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…