Related papers: Correlation and Autocorrelation of Data on Complex…

Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology,…

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…

In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…

Many real world network problems often concern multivariate nodal attributes such as image, textual, and multi-view feature vectors on nodes, rather than simple univariate nodal attributes. The existing graph estimation methods built on…

Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.

For any initial correlated network after any kind of attack where either nodes or edges are removed, we obtain general expressions for the degree-degree probability matrix and degree distribution. We show that the proposed analytical…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…

The econophysics approach to socio-economic systems is based on the assumption of their complexity. Such assumption inevitably lead to another assumption, namely that underlying interconnections within socio-economic systems, particularly…

Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…

Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…

This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…

An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated.…

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the…

Moran's index and Getis-Ord,s indices are important statistical measures of spatial autocorrelation analysis. Each of them has its own function and scope of application. However, the association of Moran index with Getis-Ord index is not…

We study the problem of estimating at a central server the mean of a set of vectors distributed across several nodes (one vector per node). When the vectors are high-dimensional, the communication cost of sending entire vectors may be…

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…

Many systems of interacting elements can be conceptualized as networks, where network nodes represent the elements and network ties represent interactions between the elements. In systems where the underlying network evolves in time, it is…