Linked | Albert-László Barabási

Summary of: Linked: The New Science Of Networks Science Of Networks
By: Albert-László Barabási

Introduction

Embark on a fascinating journey through the world of networks with Albert-László Barabási’s ‘Linked: The New Science of Networks’. This book summary offers an instructive and engaging look at the importance of networks and their underlying structures in various aspects of our lives. Discover the power of graphs, the real-world phenomenon of hubs, scale-free networks, and the concept of preferential attachments, all presented with the author’s unique insight into the complexity of our interconnected world. Prepare to have your eyes opened to the expansive and interconnected nature of the world around us, as we delve into topics ranging from the World Wide Web to social networks, with surprising associations to areas such as biology and medicine.

The Birth of Graph Theory

In the 18th century, people in the Prussian city of Königsberg tried to solve a puzzle about walking across seven bridges without crossing any twice. It stumped everyone, including mathematician Leonhard Euler, who later discovered it was impossible to solve. But in the process, he created a new field of mathematics called “graph theory.” A graph is a diagram of nodes and links, like a connect-the-dots game. Euler represented the Königsberg Bridge problem as a graph, with the four landmasses as nodes and the bridges as links. By removing inessential details, the logic of the problem became clear, leading to the birth of graph theory. Today, graphs continue to provide insights into complex phenomena, such as social networks. “Networks are present everywhere,” and all that’s needed is an eye for them.

The Small World Network

The world may seem large, but in reality, we are only separated by a few degrees.

In John Guare’s play Six Degrees of Separation, the concept that every human is only six degrees away from any other person was introduced. This idea was based on research by Harvard psychologist Stanley Milgram in 1967. Milgram conducted an experiment where he randomly selected two people from Boston and sent 160 letters to people in Wichita and Omaha, asking them to send the letters to someone who would know the targets, and so on until the targets were reached. It was found that people are on average separated by only 5.5 degrees of separation. This experiment showed that the social world is much smaller than we think.

Albert-László Barabási and his graduate students also found that the World Wide Web is a small world. They used a piece of software to map the average distance between documents on the Web and found that it only takes 19 clicks to get from one document to another. This suggests that even though the Web is big in terms of nodes, it is still a “small world” due to the high level of interconnectivity.

Small worlds are also present in other networks, such as species’ food webs, where two links are present on average between predator and prey, including when cheetahs are linked to termites via birds. Similarly, intracellular molecules have three links, and neuroscientists’ favorite worm, C. elegans, has 14 links between neurons in the brain. Networks typically have between two and 14 degrees of separation, but most real-world networks are highly interconnected.

The dense web of society creates a small world. The construction and structure of networks is the key to understanding the complex world around us. Hubs appear in most large complex networks that scientists have been able to study so far, making them a generic building block of our complex, interconnected world.

In conclusion, the idea that we are all only separated by a few degrees may seem like a clever dramatic invention, but it is a reality that has been supported by research and demonstrated in various real-world networks. We are all part of a small world network, interconnected in ways that we may not even realize.

The Power of Hubs in Scale-Free Networks

Early assumptions about networks involved random linking between nodes, with links following a Poisson distribution. However, it turns out that networks have hubs – nodes with significantly more links than others. These highly connected nodes keep the networks together, creating a power-law distribution instead of a bell-curve. This type of distribution is called a scale-free network, and it is prevalent in various fields, including digital goods, science, and Hollywood. The reason for this distribution is the unconscious bias we have to link with nodes we know, which are typically the more connected nodes. The presence of hubs in a network and the resulting power-law distribution have significant implications for understanding how networks function and how they can be optimized.

Unravelling Complex Networks

This passage explores the dynamic nature of networks and how they grow, fragment and transform. The Web is a real-world network that constantly adds nodes, resulting in the formation of hubs. However, the ‘preferential attachment’ pattern shows that nodes attach to other highly connected nodes, leading to the ‘rich get richer’ phenomenon. Although such networks don’t always result in a ‘winner takes all’ situation, the web distribution of use follows a power-law distribution. Networks also fragment due to directional links. The Web has four main continents, including a central core, IN and OUT continents, and a collection of ‘tendrils’ and free-floating ‘islands.’ The phenomenon is also observed in social networks, where like-mindedness can lead to fragmentation.

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