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The Bianconi-Barabasi model of a growing network is revisited. This model, defined by a preferential attachment rule involving both the degrees of the nodes and their intrinsic fitnesses, has the fundamental property to undergo a phase…
Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive…
The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules…
We consider a generalised d-dimensional model for asymptotically-scale-free geographical networks. Central to many networks of this kind, when considering their growth in time, is the attachment rule, i.e. the probability that a new node is…
We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
Understanding of evolutionary mechanism of online social networks is greatly significant for the development of network science. However, present researches on evolutionary mechanism of online social networks are neither deep nor clear…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
We propose a statistical method to estimate simultaneously the non-parametric transitivity and preferential attachment functions in a growing network, in contrast to conventional methods that either estimate each function in isolation or…
In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…
In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an…
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones one-by-one. At every…
The dynamical origin of complex networks, i.e., the underlying principles governing network evolution, is a crucial issue in network study. In this paper, by carrying out analysis to the temporal data of Flickr and Epinions--two typical…
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The…
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time…
We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
We consider a general class of preferential attachment schemes evolving by a reinforcement rule with respect to certain sublinear weights. In these schemes, which grow a random network, the sequence of degree distributions is an object of…
The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. We study the higher-order connectivity of such a network by investigating the topological…