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Fundamental network algorithms: A discussion of some of the most important and fundamental algorithms for performing network calculations on a computer

M. E. J. Newman

in Networks: An Introduction

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199206650
eISBN:
9780191594175
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206650.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter looks at the algorithms used to perform network calculations. It starts with some simple algorithms for calculating quantities such as degrees, degree distributions, and clustering ... More


Prolongationl Functions

Fred Lerdahl

in Tonal Pitch Space

Published in print:
2005
Published Online:
May 2008
ISBN:
9780195178296
eISBN:
9780199870370
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178296.003.0005
Subject:
Music, Theory, Analysis, Composition

This chapter elaborates a new approach to tonal and harmonic function. To do this, it establishes a frame of reference; so it first develops a tonic-finding method, based on the principle of the ... More


Minimum Paths

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0027
Subject:
Economics and Finance, Microeconomics

This is the fourth of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making, and discusses minimum paths. The eleven sections of ... More


Diatonic Space

Fred Lerdahl

in Tonal Pitch Space

Published in print:
2005
Published Online:
May 2008
ISBN:
9780195178296
eISBN:
9780199870370
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195178296.003.0002
Subject:
Music, Theory, Analysis, Composition

This chapter introduces and develops the concept of pitch space, beginning with a distinction between tonal and event hierarchies. After a consideration of previous approaches, the fundamental ... More


Small and large worlds

Sergey N. Dorogovtsev

in Lectures on Complex Networks

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199548927
eISBN:
9780191720574
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548927.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses and compares the geometries of small worlds, lattices and fractals. The first measurements of the diameter of the World Wide Web are described. The Watts–Strogatz model of a ... More


Computer algorithms

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for ... More


Consider all options, as the shortest path between two points is not always straight

Susan D'Agostino

in How to Free Your Inner Mathematician: Notes on Mathematics and Life

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198843597
eISBN:
9780191879388
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198843597.003.0013
Subject:
Mathematics, Educational Mathematics, Applied Mathematics

“Consider all options, as the shortest path between two points is not always straight” explains how to find the shortest path between two points on the globe by way of a “great circle”—an ... More


Metric and topological structure of networks

Ernesto Estrada

in The Structure of Complex Networks: Theory and Applications

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199591756
eISBN:
9780191774959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199591756.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter explains the following concepts: shortest path distance, average path length, diameter, and the small-world properties of networks in networks; resistance distance in networks; and the ... More


Mathematics of networks

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic ... More


Uncovering the Hidden Routes: Algorithms for Identifying Paths and Missing Links in Trade Networks

Constantinos Tsirogiannis and Christos Tsirogiannis

in The Connected Past: Challenges to Network Studies in Archaeology and History

Published in print:
2016
Published Online:
November 2020
ISBN:
9780198748519
eISBN:
9780191916953
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/9780198748519.003.0012
Subject:
Archaeology, History and Theory of Archaeology

A network is a simple yet powerful tool for representing a set of relations in the real world. For instance, to represent direct business relations between ... More


The structure of real-world networks

Mark Newman

in Networks

Published in print:
2018
Published Online:
October 2018
ISBN:
9780198805090
eISBN:
9780191843235
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198805090.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter brings together the ideas and techniques developed in previous chapters, applying them to a range of real-world networks to describe and understand the structure of those networks. ... More


Which Network Model Should I Use? Towards a Quantitative Comparison of Spatial Network Models in Archaeology

Tim Evans

in The Connected Past: Challenges to Network Studies in Archaeology and History

Published in print:
2016
Published Online:
November 2020
ISBN:
9780198748519
eISBN:
9780191916953
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/9780198748519.003.0015
Subject:
Archaeology, History and Theory of Archaeology

Archaeology can be ‘site centric’. Much of the primary evidence comes from excavations based on a single site so naturally the primary sources for ... More


How Reliable are Centrality Measures for Data Collected from Fragmentary and Heterogeneous Historical Sources? A Case Study

Marten Düring

in The Connected Past: Challenges to Network Studies in Archaeology and History

Published in print:
2016
Published Online:
November 2020
ISBN:
9780198748519
eISBN:
9780191916953
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/9780198748519.003.0011
Subject:
Archaeology, History and Theory of Archaeology

In social network analysis, centrality measures are used to translate empirical and common sense observations of social behaviour into mathematical ... More


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