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We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
Social networks can have asymmetric relationships. In the online social network Twitter, a follower receives tweets from a followed person but the followed person is not obliged to subscribe to the channel of the follower. Thus, it is…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
In the present work, via computational simulation we study the statistical distribution of people versus number of steps acquired by them in a learning process, considering Darwin classical theory of evolution, i.e. competition, learning…
Many networks contain correlations and often conventional analysis is incapable of incorporating this often essential feature. In arXiv:0708.2176, we introduced the link-space formalism for analysing degree-degree correlations in evolving…
To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex…
Many important real-world networks manifest "small-world" properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is "preferential attachment", where nodes…
Dynamical processes on complex networks such as information propagation, innovation diffusion, cascading failures or epidemic spreading are highly affected by their underlying topologies as characterized by, for instance, degree-degree…
In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving…
The preferential attachment (PA) process is a popular theory for explaining network power-law degree distributions. In PA, the probability that a new vertex adds an edge to an existing vertex depends on the connectivity of the target…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
We explore the interplay between the protein-protein interactions network and the expression of the interacting proteins. It is shown that interacting proteins are expressed in significantly more similar cellular concentrations. This is…
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
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…
We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction…