Related papers: Network rewiring in the $r$-$K$ plane
We develop and test a rewiring method (originally proposed by Newman) which allows to build random networks having pre-assigned degree distribution and two-point correlations. For the case of scale-free degree distributions, we discretize…
By collecting and expanding several numerical recipes developed in previous work, we implement an object-oriented Python code, based on the networkX library, for the realization of the configuration model and Newman rewiring. The software…
Degree correlation is a crucial measure in networks, significantly impacting network topology and dynamical behavior. The degree sequence of a network is a significant characteristic, and altering network degree correlation through…
We describe a procedure that allows continuously tuning the average degree $\langle k \rangle$ of uncorrelated networks with power-law degree distribution $p(k)$. Inn order to do this, we modify the low-$k$ region of $p(k)$, while…
We prove that the presence of a diagonal assortative degree correlation, even if small, has the effect of dramatically lowering the epidemic threshold of large scale-free networks. The correlation matrix considered is…
Network science have constantly been in the focus of research for the last decade, with considerable advances in the controllability of their structural. However, much less effort has been devoted to study that how to improve the…
In this work we explore degree assortativity in complex networks, and extend its usual definition beyond that of nearest neighbours. We apply this definition to model networks, and describe a rewiring algorithm that induces assortativity.…
Degree correlation is an important characteristic of networks, which is usually quantified by the assortativity coefficient. However, concerns arise about changing the assortativity coefficient of a network when networks suffer from…
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…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
We investigate two competing contact processes on a set of Watts--Strogatz networks with the clustering coefficient tuned by rewiring. The base for network construction is one-dimensional chain of $N$ sites, where each site $i$ is directly…
A tight alignment between the degree vector and the leading eigenvector arises naturally in networks with neutral degree mixing and the absence of local structures. Many real-world networks, however, violate both conditions. We derive…
The degree-degree correlation is crucial in understanding the structural properties of and dynamics occurring upon network, and is often measured by the assortativity coefficient $r$. In this paper, we first study this measure in detail and…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
The average nearest neighbor degree (ANND) of a node of degree $k$ is widely used to measure dependencies between degrees of neighbor nodes in a network. We formally analyze ANND in undirected random graphs when the graph size tends to…
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…
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
Assessing whether a given network is typical or atypical for a random-network ensemble (i.e., network-ensemble comparison) has widespread applications ranging from null-model selection and hypothesis testing to clustering and classifying…
We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is…
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…