相关论文: Pearson's correlation coefficient in the theory of…

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…

Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an…

Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…

In the present paper, we discuss the Pearson, Spearman, Kendall correlation coefficients and their statistical analogues. We propose a new correlation coefficient r and its statistical analogue. The coefficient r is based on Kendal's and…

In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…

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…

Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…

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…

Pearson's correlation coefficient is a popular statistical measure to summarize the strength of association between two continuous variables. It is usually interpreted via its square as percentage of variance of one variable predicted by…

Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…

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…

The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of…

This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and…

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 present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal…

Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…

We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…

The degree-degree correlation is important in understanding the structural organization of a network and the dynamics upon a network. Such correlation is usually measured by the assortativity coefficient $r$, with natural bounds $r \in…

This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…