Related papers: A steady state model for graph power laws
Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabasi and Albert simultaneously reproduces these properties, and…
We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…
In this paper the web is analyzed as a graph aggregated by host and pay-level domain (PLD). The web graph datasets, publicly available, have been released by the Common Crawl Foundation and are based on a web crawl performed during the…
Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
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 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…
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.…
We consider constrained ergodic resource optimization in wireless networks with graph-structured interference. We train a diffusion model policy to match expert conditional distributions over resource allocations. By leveraging a…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
The power-law behavior is ubiquitous in a majority of real-world networks, and it was shown to have a strong effect on various combinatorial, structural, and dynamical properties of graphs. For example, it has been shown that in real-life…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
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…
The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or…
Modeling Internet growth is important both for understanding the current network and to predict and improve its future. To date, Internet models have typically attempted to explain a subset of the following characteristics: network…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
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,…
Preferential attachment models are a common class of graph models which have been used to explain why power-law distributions appear in the degree sequences of real network data. One of the things they lack, however, is higher-order network…
We analyze access statistics of several popular webpages for a period of several years. The graphs of daily downloads are highly non-homogeneous with long periods of low activity interrupted by bursts of heavy traffic. These bursts are due…