Related papers: Quantifying Dismantlement in Disconnected Networks
Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against…
Disentangled representation learning plays a pivotal role in making representations controllable, interpretable and transferable. Despite its significance in the domain, the quest for reliable and consistent quantitative disentanglement…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
Measuring inconsistency is viewed as an important issue related to handling inconsistencies. Good measures are supposed to satisfy a set of rational properties. However, defining sound properties is sometimes problematic. In this paper, we…
We derive a renormalization method to calculate the spectral dimension $\bar{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of…
We investigate entanglement distribution in pure-state quantum networks. We consider the case when non-maximally entangled two-qubit pure states are shared by neighboring nodes of the network. For a given pair of nodes, we investigate how…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
With an increasing emphasis on network security, much more attention has been attracted to the vulnerability of complex networks. The multi-scale evaluation of vulnerability is widely used since it makes use of combined powers of the links'…
In this paper, we study a connection between disintegration of measures and geometric properties of probability spaces. We prove a disintegration theorem, addressing disintegration from the perspective of an optimal transport problem. We…
The reliability of a network is an important parameter to consider when building a network. Different characteristics of the network can become unreliable over time or from other outside forces. In a simple setting, we model a network as a…
Percolation theory shows that removing a small fraction of critical nodes can lead to the disintegration of a large network into many disconnected tiny subnetworks. The network dismantling task focuses on how to efficiently select the least…
Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic,…
In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network density and degree heterogeneity under…
Recent years are characterized by an unprecedented quantity of available network data which are produced at an astonishing rate by an heterogeneous variety of interconnected sensors and devices. This high-throughput generation calls for the…
We make two theoretical contributions to disentanglement learning by (a) defining precise semantics of disentangled representations, and (b) establishing robust metrics for evaluation. First, we characterize the concept "disentangled…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
Learning to disentangle and represent factors of variation in data is an important problem in AI. While many advances have been made to learn these representations, it is still unclear how to quantify disentanglement. While several metrics…
We propose a framework to analyze how multivariate representations disentangle ground-truth generative factors. A quantitative analysis of disentanglement has been based on metrics designed to compare how one variable explains each…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network…