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Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…

In a recent work \cite{LiuJoladSchZia13}, we introduced dynamic networks with preferred degrees and presented simulation and analytic studies of a single, homogeneous system as well as two interacting networks. Here, we extend these studies…

Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…

Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…

Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…

The classical preferential attachment model is sensitive to the choice of the initial configuration of the network. As the number of initial nodes and their degree grow, so does the time needed for an equilibrium degree distribution to be…

We study structural properties of trees grown by preferential attachment. In this mechanism, nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree. We classify nodes by their depth…

While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…

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…

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…

We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…

This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…

We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with…

We study the growth of bipartite networks in which the number of nodes in one of the partitions is kept fixed while the other partition is allowed to grow. We study random and preferential attachment as well as combination of both. We…

How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of…

We analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using, with probability $p$, an anti-preferential attachment mechanism or, with probability $1-p$, a…

Users of social networks display diversified behavior and online habits. For instance, a user's tendency to reply to a post can depend on the user and the person posting. For convenience, we group users into aggregated behavioral patterns,…