Related papers: A geometry-induced topological phase transition in…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…
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…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
Random geometric graphs (RGG) can be formalized as hidden-variables models where the hidden variables are the coordinates of the nodes. Here we develop a general approach to extract the typical configurations of a generic hidden-variables…
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
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…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time $t$ are distributed homogeneously between a new node and the exising nodes selected uniformly. This is…