Related papers: PageRank in Undirected Random Graphs
An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial…
A distributed algorithm performs local computations on pieces of input and communicates the results through given communication links. When processing a massive graph in a distributed algorithm, local outputs must be configured as a…
We study the Personalized PageRank (PPR) algorithm, a local spectral method for clustering, which extracts clusters using locally-biased random walks around a given seed node. In contrast to previous work, we adopt a classical statistical…
We investigate random connected graphs from a block-stable class whose distribution is weighted based on the number of $2$-connected components, or blocks. This includes the class of planar graphs. For this, we develop a notion of a…
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…
For a directed graph, the Pagerank algorithm emulates a random walker on the graph that occasionally "jumps" to a random vertex based on a jumping parameter $\alpha$. Upon completion, the algorithm generates a stochastic vector whose…
We identify the asymptotic distribution of $p$-rank of the sandpile group of a random directed bipartite graphs which are not too imbalanced. We show this matches exactly that of the Erd{\"o}s-R{\'e}nyi random directed graph model,…
How large a fraction of a graph must one explore to rank a small set of nodes according to their PageRank scores? We show that the answer is quite nuanced, and depends crucially on the interplay between the correctness guarantees one…
Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or…
Graph Neural Networks (GNNs) have achieved tremendous success in a variety of real-world applications by relying on the fixed graph data as input. However, the initial input graph might not be optimal in terms of specific downstream tasks,…
We compare two link analysis ranking methods of web pages in a site. The first, called Site Rank, is an adaptation of PageRank to the granularity of a web site and the second, called Popularity Rank, is based on the frequencies of user…
{\em Personalized PageRank (PPR)} stands as a fundamental proximity measure in graph mining. Since computing an exact SSPPR query answer is prohibitive, most existing solutions turn to approximate queries with guarantees. The…
We study the influence of network topology on retrieval properties of recurrent neural networks, using replica techniques for diluted systems. The theory is presented for a network with an arbitrary degree distribution $p(k)$ and applied to…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
In Chung-Lu random graphs, a classic model for real-world networks, each vertex is equipped with a weight drawn from a power-law distribution, and two vertices form an edge independently with probability proportional to the product of their…
We study the problem of detecting or recovering a planted ranked subgraph from a directed graph, an analog for directed graphs of the well-studied planted dense subgraph model. We suppose that, among a set of $n$ items, there is a subset…
In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank…
We give a new link spam detection and PageRank demotion algorithm called MaxRank. Like TrustRank and AntiTrustRank, it starts with a seed of hand-picked trusted and spam pages. We define the MaxRank of a page as the frequency of visit of…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
The statistical modeling of random networks has been widely used to uncover interaction mechanisms in complex systems and to predict unobserved links in real-world networks. In many applications, network connections are collected via…