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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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