Related papers: Scale-free networks with an exponent less than two
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…
A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…
In complex systems, responses to small perturbations are too diverse to predict how much they would be definitely, and then such diverse responses can be predicted in a probabilistic way. Here we study such a problem in scale-free networks,…
We study a problem of data packet transport in scale-free networks whose degree distribution follows a power-law with the exponent $\gamma$. We define load at each vertex as the accumulated total number of data packets passing through that…
Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the…
Many real-world networks display a natural bipartite structure. Investigating it based on the original structure is helpful to get deep understanding about the networks. In this paper, some real-world bipartite networks are collected and…
Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been…
Here, we propose a class of scale-free networks $G(t;m)$ with some intriguing properties, which can not be simultaneously held by all the theoretical models with power-law degree distribution in the existing literature, including (i)…
Random scale-free overlay topologies provide a number of properties like for example high resilience against failures of random nodes, small (average) diameter as well as good expansion and congestion characteristics that make them…
Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski…
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing…
There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…
We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
We study the topology of e-mail networks with e-mail addresses as nodes and e-mails as links using data from server log files. The resulting network exhibits a scale-free link distribution and pronounced small-world behavior, as observed in…
The degree distribution of a real world network -- the number of links per node -- often follows a power law, with some hubs having many more links than traditional graph generation methods predict. For years, preferential attachment and…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…