Related papers: Apollonian networks
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
Many complex networks demonstrate a phenomenon of striking degree correlations, i.e., a node tends to link to other nodes with similar (or dissimilar) degrees. From the perspective of degree correlations, this paper attempts to characterize…
Recent advancements in complex network analysis are encouraging and may provide useful insights when applied in software engineering domain, revealing properties and structures that cannot be captured by traditional metrics. In this paper,…
We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…
We numerically investigate that optimal robust onion-like networks can emerge even with the constraint of surface growth in supposing a spatially embedded transportation or communication system. To be onion-like, moderately long links are…
Voronoi and related diagrams have technological applications, for example, in motion planning and surface reconstruction, and also find significant use in materials science, molecular biology, and crystallography. Apollonius diagrams…
Networks often represent systems that do not have a long history of studies in traditional fields of physics, albeit there are some notable exceptions such as energy landscapes and quantum gravity. Here we consider networks that naturally…
In this draft paper, we introduce a novel architecture for graph networks which is equivariant to the Euclidean group in $n$-dimensions. The model is designed to work with graph networks in their general form and can be shown to include…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
This paper is an extensive survey of literature on complex network communities and clustering. Complex networks describe a widespread variety of systems in nature and society especially systems composed by a large number of highly…
The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e.…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Many real-world networks, ranging from subway systems to polymer structures and fungal mycelia, do not form by the incremental addition of individual nodes but instead grow through the successive extension and intersection of lines or…
This paper aims to establish theoretical foundations of graph product multilayer networks (GPMNs), a family of multilayer networks that can be obtained as a graph product of two or more factor networks. Cartesian, direct (tensor), and…
We investigate a Hamiltonian model of networks. The model is a mirror formulation of the XY model (hence the name) -- instead letting the XY spins vary, keeping the coupling topology static, we keep the spins conserved and sample different…
Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…
A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring…
Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted…