Related papers: Clustering Does Not Always Imply Latent Geometry

Many real-world networks were found to be highly clustered, and contain a large amount of small cliques. We here investigate the number of cliques of any size k contained in a geometric inhomogeneous random graph: a scale-free network model…

The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…

Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…

Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex…

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…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…

Citation and coauthor networks offer an insight into the dynamics of scientific progress. We can also view them as representations of a causal structure, a logical process captured in a graph. From a causal perspective, we can ask questions…

Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…

First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…

We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the…

We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,…

Systems with lattice geometry can be renormalized exploiting their coordinates in metric space, which naturally define the coarse-grained nodes. By contrast, complex networks defy the usual techniques, due to their small-world character and…

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…

Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…

A common approach to modeling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter…

The complexity of deciding whether a clustered graph admits a clustered planar drawing is a long-standing open problem in the graph drawing research area. Several research efforts focus on a restricted version of this problem where the…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…