Related papers: PageRank in scale-free random graphs
We prove logarithmic upper bounds for the diameters of the random-surfer Webgraph model and the PageRank-based selection Webgraph model, confirming the small world phenomenon holds for them. In the special case when the generated graph is a…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
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…
The Rooted Maximum Leaf Outbranching problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…
Many systems, including the Internet, social networks, and the power grid, can be represented as graphs. When analyzing graphs, it is often useful to compute scores describing the relative importance or distance between nodes. One example…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process…
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source and target nodes. Our work builds…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
The purpose of the research is to find a centrality measure that can be used in place of PageRank and to find out the conditions where we can use it in place of PageRank. After analysis and comparison of graphs with a large number of nodes…
We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the…
Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be…
Reinforcement learning has gained wide popularity as a technique for simulation-driven approximate dynamic programming. A less known aspect is that the very reasons that make it effective in dynamic programming can also be leveraged for…
After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures beside the simple linkage structure. In some scenarios we have to deal with…
We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of…
The PageRank algorithm employed at Google assigns a measure of importance to each web page for rankings in search results. In our recent papers, we have proposed a distributed randomized approach for this algorithm, where web pages are…