Related papers: Clustering in a preferential attachment network wi…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
In this paper, we study the clustering properties of the Spatial Preferential Attachment (SPA) model introduced by Aiello et al. in 2009. This model naturally combines geometry and preferential attachment using the notion of spheres of…
In this paper, we study the clustering properties of the Spatial Preferential Attachment (SPA) model. This model naturally combines geometry and preferential attachment using the notion of spheres of influence. It was previously shown in…
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…
We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree…
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…
We include complex connectivity structures and heterogeneity in models of multilayer networks or multilayer hypergraphs growing by preferential attachment. We consider the most generic connectivity structure, where the probability of…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…
In an affiliation network vertices are linked to attributes and two vertices are declared adjacent whenever they share a common attribute. For example, two customers of an internet shop are called adjacent if they have purchased the same or…
Since some realistic networks are influenced not only by increment behavior but also by tunable clustering mechanism with new nodes to be added to networks, it is interesting to characterize the model for those actual networks. In this…
We study a random graph $G_n$, which combines aspects of geometric random graphs and preferential attachment. The resulting random graphs have power-law degree sequences with finite mean and possibly infinite variance. In particular, the…
Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global…
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially…
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…
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…
In this paper, we analyze the behavior of the global clustering coefficient in scale free graphs. We are especially interested in the case of degree distribution with an infinite variance, since such degree distribution is usually observed…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…