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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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