Related papers: Growing Random Geometric Graph Models of Super-lin…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
Research on human online activities usually assumes that total activity $T$ increases linearly with active population $P$, that is, $T\propto P^{\gamma}(\gamma=1)$. However, we find examples of systems where total activity grows faster than…
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…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Urban scaling laws relate socio-economic, behavioral, and physical variables to the population size of cities and allow for a new paradigm of city planning, and an understanding of urban resilience and economies. Independently of culture…
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…
In this paper we introduce a model of spatial network growth in which nodes are placed at randomly selected locations on a unit square in $\mathbb{R}^2$, forming new connections to old nodes subject to the constraint that edges do not…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
In this paper we make an attempt to increase our understanding of the urban scaling phenomenon. We investigate how superlinear scaling emerges if a network increases in size and how this scaling depends on the occurrence of elements that…
Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here…
Urban outputs often scale superlinearly with city population. A difficulty in understanding the mechanism of this phenomenon is that different outputs differ considerably in their scaling behaviors. Here, we formulate a physics-based model…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
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…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
Research on the growth of online tagging systems not only is interesting in its own right, but also yields insights for website management and semantic web analysis. Traditional models that describing the growth of online systems can be…
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…