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JournalISSN: 1542-7951

Internet Mathematics 

Taylor & Francis
About: Internet Mathematics is an academic journal. The journal publishes majorly in the area(s): Random graph & PageRank. It has an ISSN identifier of 1542-7951. It is also open access. Over the lifetime, 250 publications have been published receiving 16160 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: The aim of this paper is to survey the ways in which Bloom filters have been used and modified in a variety of network problems, with the aim of providing a unified mathematical and practical framework for understanding them and stimulating their use in future applications.
Abstract: A Bloom filter is a simple space-efficient randomized data structure for representing a set in order to support membership queries. Bloom filters allow false positives but the space savings often outweigh this drawback when the probability of an error is controlled. Bloom filters have been used in database applications since the 1970s, but only in recent years have they become popular in the networking literature. The aim of this paper is to survey the ways in which Bloom filters have been used and modified in a variety of network problems, with the aim of providing a unified mathematical and practical framework for understanding them and stimulating their use in future applications.

2,199 citations

Journal ArticleDOI
TL;DR: A rich and long history is found of how lognormal distributions have arisen as a possible alternative to power law distributions across many fields, focusing on underlying generative models that lead to these distributions.
Abstract: Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields.

1,787 citations

Journal ArticleDOI
TL;DR: This paper employs approximation algorithms for the graph-partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities, and defines the network community profile plot, which characterizes the "best" possible community—according to the conductance measure—over a wide range of size scales.
Abstract: A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions. Rather than defining a procedure to extract sets of nodes from a graph and then attempting to interpret these sets as "real" communities, we employ approximation algorithms for the graph-partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be i...

1,660 citations

Journal ArticleDOI
TL;DR: A comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, and suggested alternatives to the traditional solution methods.
Abstract: This paper serves as a companion or extension to the "Inside PageRank" paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research.

910 citations

Journal ArticleDOI
TL;DR: In this article, a number of generalized and extended versions of concentration inequalities and martingale inequalities are examined for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and web graphs.
Abstract: We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and web graphs.

517 citations

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Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
20203
20193
20185
201714
201618
201528