Related papers: Critical phenomena on heterogeneous small-world ne…
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
Evidence of critical dynamics has been recently found in both experiments and models of large scale brain dynamics. The understanding of the nature and features of such critical regime is hampered by the relatively small size of the…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results…
Scale-free networks contain many small cliques and cycles. We model such networks as inhomogeneous random graphs with regularly varying infinite-variance weights. For these models, the number of cliques and cycles have exact integral…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the…
Traditionally, there is no evidence suggesting that there are strong ties between the rich-club property and the function of complex networks. In this study, we find that whether a very small portion of rich nodes connected to each other or…
Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of…
Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the…
We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration $t_w$ and random long-range jumps. While the time the walker needs to cover all the…
Recently Watts and Strogatz have given an interesting model of small-world networks. Here we concretise the concept of a ``far away'' connection in a network by defining a {\it far edge}. Our definition is algorithmic and independent of…
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…
We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is…
We explore a new variant of Small-World Networks (SWNs), in which an additional parameter ($r$) sets the length scale over which shortcuts are uniformly distributed. When $r=0$ we have an ordered network, whereas $r=1$ corresponds to the…
The small-world effect is a universal feature used to explain many different phenomena like percolation, diffusion, and consensus. Starting from any regular lattice of $N$ sites, the small-world effect can be attained by rewiring randomly…
The theory of graphons is an important tool in understanding properties of large networks. We investigate a power-law random graph model and cast it in the graphon framework. The distinctively different structures of the limit graph are…
We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size),…