Related papers: Power-law hypothesis for PageRank on undirected gr…
PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning.In this paper, we study PageRank in undirected random graphs with expansion property. The Chung-Lu random graph…
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…
PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning. In this paper, we study PageRank in undirected random graphs with an expansion property. The Chung-Lu random graph is…
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This…
Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged in learning problems. While most of the existing literature…
Numerous works have been proposed to generate random graphs preserving the same properties as real-life large scale networks. However, many real networks are better represented by hypergraphs. Few models for generating random hypergraphs…
In this paper, a directed network model for world-wide web is presented. The out-degree of the added nodes are supposed to be scale-free and its mean value is $m$. This model exhibits small-world effect, which means the corresponding…
Identifying the generating mechanism of a network is challenging as, more often than not, only snapshots are available, but not the full evolution. One candidate for the generating mechanism is preferential attachment which, in its simplest…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
This paper studies the distribution of a family of rankings, which includes Google's PageRank, on a directed configuration model. In particular, it is shown that the distribution of the rank of a randomly chosen node in the graph converges…
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…
Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which…
Google employs PageRank to rank web pages, determining the order in which search results are presented to users based on their queries. PageRank is primarily utilized for directed networks, although there are instances where it is also…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…
Mixing patterns in large self-organizing networks, such as the Internet, the World Wide Web, social and biological networks are often characterized by degree-degree {dependencies} between neighbouring nodes. One of the problems with the…
Leaf powers and $k$-leaf powers have been studied for over 20 years, but there are still several aspects of this graph class that are poorly understood. One such aspect is the leaf rank of leaf powers, i.e. the smallest number $k$ such that…
In network theory, Pearson's correlation coefficients are most commonly used to measure the degree assortativity of a network. We investigate the behavior of these coefficients in the setting of directed networks with heavy-tailed degree…