Related papers: Recursive graphs with small-world scale-free prope…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This…
The community structure and motif-modular-network hierarchy are of great importance for understanding the relationship between structures and functions. In this paper, we investigate the distribution of clique-degree, which is an extension…
We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Real-world networks often have power-law degrees and scale-free properties such as ultra-small distances and ultra-fast information spreading. In this paper, we study a third universal property: three-point correlations that suppress the…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
We propose a deterministic weighted scale-free small-world model for considering pseudofractal web with the coevolution of topology and weight. In the model, we have the degree distribution exponent $\gamma$ restricted to a range between 2…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent…
Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing…
Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…
We study the statistical properties of the generation of random graphs according the configuration model, where one assigns randomly degrees to nodes. This model is often used, e.g., for the scale-free degree distribution ~d^gamma. For the…
The clique graph $kG$ of a graph $G$ has as its vertices the cliques (maximal complete subgraphs) of $G$, two of which are adjacent in $kG$ if they have non-empty intersection in $G$. We say that $G$ is clique convergent if $k^nG\cong k^m…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free…
We show that not only preferential attachment but also preferential depletion leads to scale-free networks. The resulting degree distribution exponents is typically less than two (5/3) as opposed to the case of the growth models studied…