相关论文: A geometric growth model interpolating between reg…

Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…

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…

We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…

Performing signal processing over graphs requires knowledge of the underlying fixed topology. However, graphs often grow in size with new nodes appearing over time, whose connectivity is typically unknown; hence, making more challenging the…

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…

Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…

We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network…

This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be…

We propose a generative graph model for electrical infrastructure networks that accounts for heterogeneity in both node and edge type. To inform the model design, we analyze the properties of power grid graphs derived from the U.S. Eastern…

The Watts-Strogatz algorithm of transferring the square lattice to a small world network is modified by introducing preferential rewiring constrained by connectivity demand. The evolution of the network is two-step: sequential preferential…

Motivated by results of Henry, Pralat and Zhang (PNAS 108.21 (2011): 8605-8610), we propose a general scheme for evolving spatial networks in order to reduce their total edge lengths. We study the properties of the equilbria of two networks…

We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first…

We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…

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 study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…

The topological (or graph) structures of real-world networks are known to be predictive of multiple dynamic properties of the networks. Conventionally, a graph structure is represented using an adjacency matrix or a set of hand-crafted…

Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is…

Cell fate decisions emerge as a consequence of a complex set of gene regulatory networks. Models of these networks are known to have more parameters than data can determine. Recent work, inspired by Waddington's metaphor of a landscape, has…

In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…