Related papers: Spatial networks evolving to reduce length
Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
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.…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
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…
Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…
A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…
Multi-layered social networks consist of the fixed set of nodes linked by multiple connections. These connections may be derived from different types of user activities logged in the IT system. To calculate any structural measures for…
We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging…
Network theory provides novel concepts that promise an improved characterization of interacting dynamical systems. Within this framework, evolving networks can be considered as being composed of nodes, representing systems, and of…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new…
Networks are everywhere and their many types, including social networks, the Internet, food webs etc., have been studied for the last few decades. However, in real-world networks, it's hard to find examples that can be easily comparable,…
Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present an evolutionary algorithm for reconstruction of…
In this paper we show how Group Equivariant Convolutional Neural Networks use subsampling to learn to break equivariance to their symmetries. We focus on 2D rotations and reflections and investigate the impact of broken equivariance on…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
In the classic model of first passage percolation, for pairs of vertices separated by a Euclidean distance $L$, geodesics exhibit deviations from their mean length $L$ that are of order $L^\chi$, while the transversal fluctuations, known as…
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…