Related papers: Pearson Correlations on Networks: Corrigendum
Resistance distance has been studied extensively in the past years, with the majority of previous studies devoted to undirected networks, in spite of the fact that various realistic networks are directed. Although several generalizations of…
We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation…
We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree…
A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
Journal rankings are widely used and are often based on citation data in combination with a network perspective. We argue that some of these network-based rankings can produce misleading results. From a theoretical point of view, we show…
In numerous physical models on networks, dynamics are based on interactions that exclusively involve properties of a node's nearest neighbors. However, a node's local view of its neighbors may systematically bias perceptions of network…
A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…
Stimulated by the growing interest in the applications of complex networks framework on time series analysis, we devise a network model in which each of $N$ nodes is associated with a random walk of length $L$. Connectivity between any two…
Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…
The problem of measuring similarity of graphs and their nodes is important in a range of practical problems. There is a number of proposed measures, some of them being based on iterative calculation of similarity between two graphs and the…