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The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
The ability to sample random networks that can accurately represent real social contact networks is essential to the study of viral epidemics. The Barab\'asi-Albert model and its extensions attempt to capture reality by generating networks…
In many networks of scientific interest we know that the link between any pair of vertices conforms to a specific probability, such as the link probability in the Barab\'asi-Albert scale-free networks. Here we demonstrate how the…
Correlation between nodes is found to be a common and important property in many complex networks. Here we investigate degree correlations of the Barabasi-Albert (BA) Scale-Free model with both analytical results and simulations, and find…
A Barab\'asi-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The cost function, which is the total wiring…
There are a number of existing studies analysing the convergence behaviour of graph neural networks on large random graphs. Unfortunately, the majority of these studies do not model correlations between node features, which would naturally…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…
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…
A network is scale-free if its connectivity density function is proportional to a power-law distribution. Scale-free networks may provide an explanation for the robustness observed in certain physical and biological phenomena, since the…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
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…
All crucial features of the recently observed real-world weighted networks are obtained in a model where the weight of a link is defined with a single non-linear parameter $\alpha$ as $w_{ij}=(s_is_j)^\alpha$, $s_i$ and $s_j$ are the…
Many real networks such as the World Wide Web, financial, biological, citation and social networks have a power-law degree distribution. Networks with this feature are also called scale-free. Several models for producing scale-free networks…
This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…
We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
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…