Related papers: The Topological Behavior of Preferential Attachmen…
Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behaviour, which are known to depend on topology, can also be explored by tuning the form of the…
The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
The propensity for synchronization is studied in a complex network of asymmetrically coupled units, where the asymmetry in a given link is determined by the relative age of the involved nodes. In growing scale-free networks synchronization…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
We present a statistical analysis of different metrics characterizing the topological properties of Internet maps, collected at two different resolution scales: the router and the autonomous system level. The metrics we consider allow us to…
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
Path homology is a topological invariant for directed graphs, which is sensitive to their asymmetry and can discern between digraphs which are indistinguishable to the directed flag complex. In Erd\"os-R\'enyi directed random graphs, the…
A road map to understand the relation between the onset of the superconducting state with the particular optimum heterogeneity in granular superconductors is to study a Random Tranverse Ising Model on complex networks with a scale-free…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…
A topological approach to the theory of equilibrium phase transitions in statistical physics is based on the Topological Hypothesis (TH), which claims that phase transitions are due to changes of the topology of suitable submanifolds in the…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices,…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…