Related papers: PageRank of integers
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…
Looking into the growth of information in the web it is a very tedious process of getting the exact information the user is looking for. Many search engines generate user profile related data listing. This paper involves one such process…
Inspired by the PageRank and HITS (hubs and authorities) algorithms for Web search, we propose a structural re-ranking approach to ad hoc information retrieval: we reorder the documents in an initially retrieved set by exploiting asymmetric…
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…
To identify communities in directed networks, we propose a generalized form of modularity in directed networks by introducing a new quantity LinkRank, which can be considered as the PageRank of links. This generalization is consistent with…
As a measure of vertex importance according to the graph structure, PageRank has been widely applied in various fields. While many PageRank algorithms have been proposed in the past decades, few of them take into account whether the graph…
We performed a large-scale crawl of the World Wide Web, covering 6.9 Million domains and 57 Million subdomains, including all high-traffic sites of the Internet. We present a study of the correlations found between quantities measuring the…
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each…
In this article we will present a graph partitioning algorithm which partitions a graph into two different types of components: the well-known `strongly connected components' as well as another type of components we call `connected acyclic…
Semantic networks qualify the meaning of an edge relating any two vertices. Determining which vertices are most "central" in a semantic network is difficult because one relationship type may be deemed subjectively more important than…
With the rise of social networks, information on the internet is no longer solely organized by web pages. Rather, content is generated and shared among users and organized around their social relations on social networks. This presents new…
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…
Matrix functions play an important role in applied mathematics. In network analysis, in particular, the exponential of the adjacency matrix associated with a network provides valuable information about connectivity, as well as about the…
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…
Homophily is the principle whereby "similarity breeds connections". We give a quantitative formulation of this principle within networks. Given a network and a labeled partition of its vertices, the vector indexed by each class of the…
Relying on the idea that back-of-the-book indexes are traditional devices for navigation through large documents, we have developed a method to build a hypertextual network that helps the navigation in a document. Building such an…
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by their popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network…
In this paper some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered, by showing that…
Random matrices arise in many mathematical contexts, and it is natural to ask about the properties that such matrices satisfy. If we choose a matrix with integer entries at random, for example, what is the probability that it will have a…
Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…