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Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
One of the best-known models in network science is preferential attachment. In this model, the probability of attaching to a node depends on the degree of all nodes in the population, and thus depends on global information. In many…
Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…
The principle that 'the brand effect is attractive' underlies preferential attachment. Here we show that the brand effect is just one dimension of attractiveness. Another dimension is competitiveness. We firstly develop a general framework…
Global Neuron Importance Estimation is used to prune neural networks for efficiency reasons. To determine the global importance of each neuron or convolutional kernel, most of the existing methods either use activation or gradient…
Abstract In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but…
The degree distribution is a key statistical indicator in network theory, often used to understand how information spreads across connected nodes. In this paper, we focus on non-growing networks formed through a rewiring algorithm and…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
Modeling networks can serve as a means of summarizing high-dimensional complex systems. Adapting an approach devised for dense, weighted networks, we propose a new method for generating and estimating unweighted networks. This approach can…
Estimating the probabilities of linkages in a network has gained increasing interest in recent years. One popular model for network analysis is the exchangeable graph model (ExGM) characterized by a two-dimensional function known as a…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
Preferential attachment (PA) models of network structure are widely used due to their explanatory power and conceptual simplicity. PA models are able to account for the scale-free degree distributions observed in many real-world large…
Self-organization of robust and efficient networks is important for a future design of communication or transportation systems, because both characteristics are not coexisting in many real networks. As one of the candidates for the…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
Popularity is attractive -- this is the formula underlying preferential attachment, a popular explanation for the emergence of scaling in growing networks. If new connections are made preferentially to more popular nodes, then the resulting…
Complex systems can be characterized by classes of equivalency of their elements defined according to system specific rules. We propose a generalized preferential attachment model to describe the class size distribution. The model…
The exponential-family random graph models (ERGMs) have emerged as an important framework for modeling social networks for a wide variety of relational types. ERGMs for valued networks are less well-developed than their unvalued…
The preferential attachment (PA) process is a popular theory for explaining network power-law degree distributions. In PA, the probability that a new vertex adds an edge to an existing vertex depends on the connectivity of the target…