The New Science of Networks

By: Albert-Laszlo Barabasi.

Published: 2002.

Read: 2019.

Summary:

The central thesis of this book is that in order to understand how complex systems work, you can’t just study its ever smaller parts. Understanding its parts will not tell you anything about the countless many ways in which these parts can be “put back together”.

You need to understand and study how the individual parts interact and how they are connected. How the system is linked together, the structure of its network.

Worth Reading:

Interesting discussion of the history of network theory with practical examples of its applications (the Internet, cell biology, industry structure, communities, etc.). A clear description of some of the basic concepts, specifically the importance of hubs in networks and the special case of scale free networks.

Other books (Ubiquity, At Home in the Universe, The Vital Question) probably dig a little deeper and explore related subjects such as how emerging networks self-organize, learn and balance the need for stability and adaptability.

Practical Takeaways:

• The rich get richer, the fit get fitter.
  • If a system grows and its parts sufficiently differ.
  • Most parts have only a few connections (friends).
  • Some have many (acquaintances).
• Hubs (acquaintances) spread information.
  • Provide access to information from outside your own clusters.
  • Helpful to have friends (connections within your cluster).
  • Helpful to have acquaintances (connections outside of your cluster).

Key Concepts:

• Complex systems are networks.
  • Consist of parts connected and interacting with each other.
• As networks grow, clusters form.
  • More parts, more links.
  • After a critical number of parts are linked, clusters emerge.
• Even very large networks act like “small worlds”.
  • Takes only a few steps to go from any one part to another.
  • “Six degrees of separation”.
• Hubs allows big networks to act like “small worlds”.
  • Most parts have only a few links.
    • Mostly to other parts within the same cluster (‘best friends’).
  • Hubs have a large number of links.
    • Including some links to other clusters (‘acquaintances’).
  • Hubs shorten paths and allow information to flow.
  • A few hubs to drastically reduce the distance between all parts.
• Hubs form when networks grow.
  • Growth = new parts to the network.
  • Preferential attachment: new parts attach to parts already well connected.
  • The rich get richer.
• Preferential attachment is driven by variety in fitness.
  • Applies when parts differ in terms of fitness.
  • Parts with a higher fitness are linked to more frequently.
  • The fit get fitter.
• When the variety of fitness is high: scale-free networks.
  • If parts look the same:
    • Parts will link randomly.
    • Every part will have about the same number of links.
    • No hubs will develop.
    • Not very interesting.
  • If parts are very different:
    • Preferential attachment.
    • Many parts have a few connections.
    • Few parts have many connections.
    • Formation of hubs.
    • Scale free networks: “power law”, hierarchy of connected parts.
• Scale free networks are robust against general failure…
  • Most parts have very few connections.
  • Generally remove any part, likely to remove a poorly connected part.
  • Low chance of removing a well connected hub.
  • Network is unlikely to be affected.
• … but fragile against specific attacks…
  • Some parts (hubs) have many connections.
  • Specifically remove the most connected part.
  • Network can fail very quickly and cause a cascade of failure.
• … and can spread information very quickly:
  • Hubs have many connections.
  • Easily reached (or infected).
  • Can distribute information very easily.