The low distances, on the other hand, mean that there is a short chain of social connections between any two people (this effect is known as six degrees of separation).
In the context of a social network, this results in the small world phenomenon of strangers being linked by a short chain of acquaintances.
[3] A certain category of small-world networks were identified as a class of random graphs by Duncan Watts and Steven Strogatz in 1998.
Watts and Strogatz measured that in fact many real-world networks have a small average shortest path length, but also a clustering coefficient significantly higher than expected by random chance.
[5] This work was followed by many studies, including exact results (Barrat and Weigt, 1999; Dorogovtsev and Mendes; Barmpoutis and Murray, 2010).
The number of degrees of separation between Albert Einstein and Alexander the Great is almost certainly greater than 30[15] and this network does not have small-world properties.
The number of times a message changed hands in the days of the visual telegraph (circa 1800–1850) was determined by the requirement that two stations be connected by line-of-sight.
It is hypothesized by some researchers, such as Albert-László Barabási, that the prevalence of small world networks in biological systems may reflect an evolutionary advantage of such an architecture.
For example, if the small airport in Sun Valley, Idaho was shut down, it would not increase the average number of flights that other passengers traveling in the United States would have to take to arrive at their respective destinations.
However, if random deletion of a node hits a hub by chance, the average path length can increase dramatically.
These approaches are based on edge-dual transformation and can be used to generate analytically solvable small-world network models for research into these systems.
Constructing such small-world networks is done as part of the effort to find graphs of order close to the Moore bound.
Small-world properties can arise naturally in social networks and other real-world systems via the process of dual-phase evolution.
[22] The advantages to small world networking for social movement groups are their resistance to change due to the filtering apparatus of using highly connected nodes, and its better effectiveness in relaying information while keeping the number of links required to connect a network to a minimum.
[23] The small world network model is directly applicable to affinity group theory represented in sociological arguments by William Finnegan.
This small world model has proven an extremely effective protest organization tactic against police action.
A practical example of this is small world networking through affinity groups that William Finnegan outlines in reference to the 1999 Seattle WTO protests.
[27][28] The greater the database links align to a small-world network the more likely a user is going to be able to extract information in the future.
Nearest Neighbor Search solutions like HNSW use small-world networks to efficiently find the information in large item corpuses.
Structural and functional connectivity in the brain has also been found to reflect the small-world topology of short path length and high clustering.
[34] The network structure has been found in the mammalian cortex across species as well as in large scale imaging studies in humans.
[39] Loss of small-world network structure has been found to indicate changes in cognition and increased risk of psychological disorders.
A computer model developed by Sara Solla[40][41] had two stable states, a property (called bistability) thought to be important in memory storage.