I have recently finished reading Linked, a great book by Albert-László Barabási about the network theory and its applications (see my review here). I recommend checking out this book to everyone, as a teaser I’d like to share with you some insights I gained about the networks, and specifically the network models, qualities and applications.
- Network science is based on graph theory, which was first conceived by Leonhard Euler. Euler developed it as a tool to solve the Konigsberg bridges challenge.
- Random network theory, developed by Erdos and Renyi, mathematically proves that in any group it requires on average 1 link per person to make the entire group fully connected.
- The clustered network model developed by Watts and Strogatz shows how the introduction of a few long-range links (weak ties) makes every network a small world (characterized by a small degree of separation).
- The power law distribution of scale-free networks proves the existence of hubs – several highly connected nodes, such as the influencers in the online world.
- Clustering coefficient determines the level of interconnectedness of a network or a network’s module.
- The degree exponent on a scale-free network tells us how many hubs (popular nodes) there are relative to the other (less popular) nodes.
- Growth and preferential attachment are the conditions that create scale-free networks.
- Fitness model describes how a recently new node can turn very popular (become a hub).
- The fitness distribution can lead to two types of behavior: fit-get-rich, or winner-takes-all.
- When it comes to finding a job, launching a business, or spreading the latest fad, our weak social ties are more important than strong ties (such as between friends or family).
- Most of the real, complex networks (such as the Internet, the Web, human cell, society, etc.) are characterized by power law distribution, and therefore are best described by the scale-free model.
- Scale-free networks are topologically robust, meaning that they have high error tolerance. However, this same topology results also in high vulnerability to attacks, as eliminating the hubs quickly breaks the whole network apart.
- Cascading failures can quickly affect the whole network. This can be visible for example in spreading of epidemics, computer viruses, or in financial crises.
- The adoption of innovations depends on the behavior of opinion leaders (the influencers, or hubs in the social network), spreading rate, and the critical threshold, which can be described in terms of network theory.
- To effectively stop spreading a contagious disease, we should first target the hubs – highly connected individuals.
This list is only a selection of hundreds of knowledge gems, for more of them I recommend you read Linked!