Related papers: Quantification and Comparison of Degree Distributi…
There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this work, we show that degree dispersion -- the fact that the…
We develop a local probe to estimate the connectivity of complex quantum networks. Our results show how global properties of different classes of complex networks can be estimated - in quantitative manner with high accuracy - by coupling a…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…
A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that…
We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…
It is well-known that the scale-free networks are ubiquitous in nature and society and have been one of the hotspot topic in complex networks. Recently, scholars presented a large quantity of scale-free networks by calculating cumulative…
Robust and comprehensive characterization of the topological properties of complex networks requires the adoption of several respective measurements, among which the node degree has special importance. In the present work, we provide an…
Owing to their capability of summarising interactions between elements of a system, networks have become a common type of data in many fields. As networks can be inhomogeneous, in that different regions of the network may exhibit different…
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not),…
We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…
Quantification is well known to be a major obstacle in the construction of a probabilistic network, especially when relying on human experts for this purpose. The construction of a qualitative probabilistic network has been proposed as an…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the…
We investigate a variety of statistical properties associated with the number of distinct degrees that exist in a typical network for various classes of networks. For a single realization of a network with N nodes that is drawn from an…
Understanding the flow of information in Deep Neural Networks (DNNs) is a challenging problem that has gain increasing attention over the last few years. While several methods have been proposed to explain network predictions, there have…
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of…