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9. All the world’s a net; or not?

9. All the world’s a net; or not?  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0009
Item type: 
chapter
ISBN: 
9780199588077
‘All the world's a net; or not?’ summarizes the extent and limitations of network science. There are warnings about the generalizations drawn from network theory, but the results of network ... More
4. A combinatorial zoo

4. A combinatorial zoo  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0004
Item type: 
chapter
ISBN: 
9780198723493
‘A combinatorial zoo’ presents a menagerie of combinatorial topics, ranging from the box (or pigeonhole) principle, the inclusion–exclusion principle, the derangement problem, and the Tower ... More
4. Connected and close

4. Connected and close  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0004
Item type: 
chapter
ISBN: 
9780199588077
‘Connected and close’ shows almost all the elements of networks take part in one large connected structure, called a giant connected component. Almost every node has a path of connections ... More
8. Designs and geometry

8. Designs and geometry  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0008
Item type: 
chapter
ISBN: 
9780198723493
Block designs are used when designing experiments in which varieties of a commodity are compared. ‘Designs and geometry’ introduces various types of block design, and then relates them to ... More
7. Digging deeper into networks

7. Digging deeper into networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0007
Item type: 
chapter
ISBN: 
9780199588077
‘Digging deeper into networks’ shows that to capture the more subtle structure of networks one has to find measures that describe the surroundings of a node — degree distribution is not ... More
6. Emergence of networks

6. Emergence of networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0006
Item type: 
chapter
ISBN: 
9780199588077
‘Emergence of networks’ considers a range of network models that explain how local mechanisms, without global planning, can generate large-scale, complex, ordered, and efficient structures. ... More
2. Four types of problem

2. Four types of problem  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0002
Item type: 
chapter
ISBN: 
9780198723493
‘Four types of problem’ explains that combinatorics is concerned with four types of problem: existence problems (does x exist?); construction problems (if x exists, how can we construct ... More
2. A fruitful approach

2. A fruitful approach  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0002
Item type: 
chapter
ISBN: 
9780199588077
‘A fruitful approach’ shows how the vertices and edges of graphs identify relations between things and how Jacob Moreno became the first to apply this to the analysis of social networks ... More
6. Graphs

6. Graphs  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0006
Item type: 
chapter
ISBN: 
9780198723493
Graph theory is about collections of points that are joined in pairs, such as a road map with towns connected by roads or a molecule with atoms joined by chemical bonds. ‘Graphs’ revisits ... More
1. A network point of view on the world

1. A network point of view on the world  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0001
Item type: 
chapter
ISBN: 
9780199588077
On a typical day, we check emails, update social network profiles, make mobile phone calls, use public transportation, take planes, and transfer money and goods. In all these cases — ... More
9. Partitions

9. Partitions  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0009
Item type: 
chapter
ISBN: 
9780198723493
How many ways can a number be split into two, three, or more pieces? ‘Partitions’ considers this interesting problem and the way in which Leonard Euler started to investigate them around ... More
8. Perfect storms in networks

8. Perfect storms in networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0008
Item type: 
chapter
ISBN: 
9780199588077
‘Perfect storms in networks’ shows that the range of possible dynamics in networks is enormous. Domino effects, co-extinctions, cascading failures, breakdown avalanches, systemic failure of ... More
3. Permutations and combinations

3. Permutations and combinations  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0003
Item type: 
chapter
ISBN: 
9780198723493
Permutations and combinations have been studied for thousands of years. ‘Permutations and combinations’ considers selecting objects from a collection, either in a particular order (such as ... More
7. Square arrays

7. Square arrays  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0007
Item type: 
chapter
ISBN: 
9780198723493
‘Square arrays’ is concerned with magic squares and latin squares. An n × n magic square, or a magic square of order n, is a square array of numbers (usually the numbers from 1 to n ... More
5. Superconnectors

5. Superconnectors  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0005
Item type: 
chapter
ISBN: 
9780199588077
‘Superconnectors’ compares homogeneous networks, where all nodes have more or less the same degree, and heterogeneous networks, where hubs, or superconnectors, are present. In homogeneous ... More
5. Tilings and polyhedra

5. Tilings and polyhedra  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0005
Item type: 
chapter
ISBN: 
9780198723493
A tiling of the plane (or tessellation) is a covering of the whole plane with tiles so that no tiles overlap and there are no gaps. Polyhedra are three-dimensional solids that are bounded ... More
1. What is combinatorics?

1. What is combinatorics?  

Robin Wilson

in Combinatorics: A Very Short Introduction

Print Publication Year: 
Apr 2016
Published Online: 
Apr 2016
eISBN: 
9780191790324
DOI: 
10.1093/actrade/9780198723493.003.0001
Item type: 
chapter
ISBN: 
9780198723493
Combinatorics can loosely be described as the branch of mathematics concerned with selecting, arranging, constructing, classifying, and counting or listing things. ‘What is combinatorics?’ ... More
3. A world of networks

3. A world of networks  

Guido Caldarelli and Michele Catanzaro

in Networks: A Very Short Introduction

Print Publication Year: 
Oct 2012
Published Online: 
Sep 2013
eISBN: 
9780191777936
DOI: 
10.1093/actrade/9780199588077.003.0003
Item type: 
chapter
ISBN: 
9780199588077
‘A world of networks’ considers how the world's networks are interconnected. In cyberspace, power grids support the Internet, which hosts the WWW, which in turn enables email services, ... More

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