Monthly Archives: October 2012

Networks’ resilience


Stories from a connected world – Networks’ resilience

In July 2001, a train derailed [PDF] in a Maryland tunnel , causing a fire. The fire fused optical fibers in the tunnel and, after a short time, Internet traffic slowed down in part of the United States. It is uncommon that an accident reduces macroscopically the efficiency of the Internet. At any given time, thousands of routers are out of use. However, the network seems to tolerate smoothly this chronic malfunction.

This extraordinary resilience appears in many other systems structured as networks. Social groups such as companies or institutions always suffer communication problems. However, they manage to carry on complicated tasks such as building an airplane or collecting taxes. Many species become extinct by natural selection. However, the biosphere continues working. Genetic mutations are ordinary events. But organisms show tremendous strength, even when there are mutations that lead to the disappearance of a large number of proteins.

Several groups of researchers have performed computer simulations to see how many nodes of the Internet would have to  be removed to stop it working. Surprisingly, even after removing 80% of them, the network remains connected. To understand this result, researchers have undertaken the same experiment with an artificial network, in which the superconnected nodes of the Internet are missing. In this case, the network fragments much faster. The presence of superconnectors is the key to the high resilience of many networks.

Want to know more? Read “Networks. A Very Short Introduction

(Movie adapted from “Einstein a la platja”. Thanks to Barcelona Televisió)

The web of life


Stories from a connected world – The web of life

Thousands of species disappear every year. The extinction of a species can affect many others, because the ecosystem has the structure of a network. Let’s look at an example.

In the early twentieth century, sea otters off the coast of California had almost disappeared because of hunting. In 1911, the U.S. government decided to protect them. Sea otters proliferated and fed abundantly on their main prey, sea urchins. The sea urchin population declined, which increased the amount of algae, their favourite food. With the renewed abundance of algae, more food became available for a range of fishes and coastal erosion was reduced. Avoiding extinction triggered a domino-effect.

Understanding ecosystems is not always easy. In the 1980s, the population of cod in the North Atlantic declined remarkably. Canadian stakeholders blamed seals, for being predators of cods. Although many seals were killed, the cod population continued to decline. In the late ’90s, ecologists drew the food chains that connect the seal and the cod, and obtained a dense and intricate picture [PDF], It was much more complex than it was supposed to be. An ecosystem is a network and, in order to understand it, one has to take into account the pattern of its connections.

“Networks. A Very Short Introduction” is out!

Today is the official publication date of my book on networks:

G. Caldarelli, M. Catanzaro “Networks. A Very Short Introduction” Oxford University Press. (US website)

SUMMARY: From ecosystems to Facebook and from the Internet to the global financial market, networks play a central role in nature and society. Phenomena such as climate change, pandemics, and financial crises are based on networked structures; and networks give insights into how social environments affect health and behaviour. In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using familiar examples from society, technology, nature, and history. They show how networks self-organize and the role they play in processes like large-scale blackouts and computer virus outbreaks. They also describe the wide and important applications of network theory in a range of areas, including genetics, ecology, technology, and management.

Find in the following links a short video and a blogpost on the subject.

How to get it (£7.99, $11.95)

  • Bookshops in UK and USA.
  • Bookshops in Spain. Possibly, in La Central and Laie in the next few days: if you are interested, write at catanzaro [DOT] michele [AT] gmail [DOT] com and I will alert you when the book is available there.
  • Amazon UK (Amazon US).
  • Other online booksellers (for example Barnes&Noble).
  • Ebook. Soon available for Kindle, Nook, Sony,, Google Play, and Kobo : if you are interested, write at catanzaro [DOT] michele [AT] gmail [DOT] com and I will alert you when the book is available.

To know more about networks:

It’s a small world!



Stories from a connected world – It’s a small world!

I’m sure you have experienced meeting a stranger at a party, and finding that she is a friend of a schoolmate of yours, or an acquaintance of a relative, or a football teammate of a co-worker. This experience is not so weird as it seems.

In 1967, psychologist Stanley Milgram showed that the expression “it’s a small world” is not just a cliché. Milgram sent tens of letters to random US citizens, and asked them to forward the letters to a person in Boston. The address was not given. Participants in the experiment [PDF] were asked to send the letter to some acquaintance that could be somehow “close” to the recipient. It seemed a hopeless task, but after a few days the recipient in Boston started to get the first letters. By the end of the experiment, more than half of the letters had arrived, through only six intermediaries, on average.

The number six is not that important, as different numbers appear by repeating the experiment. What is surprising is that these numbers are always very small. Playwright John Guare wrote:   “Everybody on this planet is separated by only six other people. The president of the United States. A gondolier in Venice. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people.”

Want to know more? Read “Networks. A Very Short Introduction

The value of networks

How can Facebook make hundreds of thousands of US citizens go to vote? Why does Lionel Messi perform better in FC Barcelona than in Argentina? Can we forecast financial crises or global epidemics? How did Cosimo de’ Medici got to power and how can you get a job? Networks are the answers to many of this questions. This post on OUP blog by G. Caldarelli and me explains how.