Related papers: Scaling laws in empirical networks

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…

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but…

Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…

We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…

The performance of a language model has been shown to be effectively modeled as a power-law in its parameter count. Here we study the scaling behaviors of Routing Networks: architectures that conditionally use only a subset of their…

Modeling human dynamics responsible for the formation and evolution of the so-called social networks - structures comprised of individuals or organizations and indicating connectivities existing in a community - is a topic recently…

A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…

Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…

Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…

Empirical complex systems must differentially respond to external perturbations and, at the same time, internally distribute information to coordinate their components. While networked backbones help with the latter, they limit the…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this…

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…