Related papers: Measuring degree-degree association in networks
Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research…
Although most of the real networks contain a mixture of directed and bidirectional (reciprocal) connections, the reciprocity $r$ has received little attention as a subject of theoretical understanding. We study the expected reciprocity of…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
We obtained Pearson's coefficient of strongly correlated recursive networks growing by preferential attachment of every new vertex by $m$ edges. We found that the Pearson coefficient is exactly zero in the infinite network limit for the…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
Given a set of people and a set of events they attend, we address the problem of measuring connectedness or tie strength between each pair of persons given that attendance at mutual events gives an implicit social network between people. We…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
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…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
In recent decades, a number of centrality metrics describing network properties of nodes have been proposed to rank the importance of nodes. In order to understand the correlations between centrality metrics and to approximate a…
We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…
George R. Terrell (1983, {Ann. Probab., vol. 11(3), pp. 823--826) showed that the Pearson coefficient of correlation of an ordered pair from a random sample of size two is at most one-half, and the equality is attained only for rectangular…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
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…