Related papers: Power Law Distributions in Class Relationships

The gap between data production and user ability to access, compute and produce meaningful results calls for tools that address the challenges associated with big data volume, velocity and variety. One of the key hurdles is the inability to…

Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…

We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…

It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…

Power-law distributions are widely recognized in complex systems physics as indicative of underlying complexity in interaction networks and critical macroscopic behavior. Previous studies, notably those of Newman and others, have emphasized…

The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…

The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…

We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that…

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…

We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are…

Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…

Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of…

Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explicated. We investigate the dynamic behaviors of resource/traffic flow on scale-free…

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

We bring rigor to the vibrant activity of detecting power laws in empirical degree distributions in real-world networks. We first provide a rigorous definition of power-law distributions, equivalent to the definition of regularly varying…

We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…