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## Social Interactions: Theory and Empirics

*Yannis M. Ioannides*

### in From Neighborhoods to Nations: The Economics of Social Interactions

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691126852
- eISBN:
- 9781400845385
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691126852.003.0002
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter discusses the theory and empirics of social interactions, with particular emphasis on the role of social context in individual decisions. It begins by introducing a sequence of models ... More

## Graph Theory: A Look Back—The Road Ahead

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0013
- Subject:
- Mathematics, Applied Mathematics

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution ... More

## Urban Magic: Concluding Remarks

*Yannis M. Ioannides*

### in From Neighborhoods to Nations: The Economics of Social Interactions

- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691126852
- eISBN:
- 9781400845385
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691126852.003.0010
- Subject:
- Economics and Finance, Development, Growth, and Environmental

This chapter considers the prospect of a deeper understanding of social interactions in urban settings as well as their significance for the functioning and future role of cities and regions. It ... More

## The Fascinating World of Graph Theory

*Ping Zhang, Gary Chartrand, and Arthur Benjamin*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.001.0001
- Subject:
- Mathematics, Applied Mathematics

Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, ... More

## Introducing Graphs

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter provides an introduction to graphs, a mathematical structure for visualizing, analyzing, and generalizing a situation or problem. It first consider four problems that have a distinct ... More

## The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

*Jason Rosenhouse and Jennifer Beineke (eds)*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691171920
- eISBN:
- 9781400889136
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171920.001.0001
- Subject:
- Mathematics, History of Mathematics

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, ... More

## Synchronizing Graphs

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0012
- Subject:
- Mathematics, Applied Mathematics

This chapter considers a new type of graph coloring known as edge coloring. It begins with a discussion of an idea by Scottish physicist Peter Guthrie Tait that led to edge coloring. Tait proved that ... More

## Orienting Graphs

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0009
- Subject:
- Mathematics, Applied Mathematics

This chapter focuses on oriented graphs and their use to represent a sports tournament where assigning a direction to an edge represents the defeat of one team by another. It first considers the 1941 ... More

## Making Walks Count: From Silent Circles to Hamiltonian Cycles

*Max A. Alekseyev and Gérard P. Michon*

### in The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691171920
- eISBN:
- 9781400889136
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171920.003.0010
- Subject:
- Mathematics, History of Mathematics

Leonhard Euler (1707–1783) invented graph theory in 1735, by solving a puzzle of interest to the inhabitants of Königsberg. The city comprised three distinct land masses, connected by seven bridges. ... More

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