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In the days when the post was carried by hand or on horseback, the number of times a letter changed hands between its source and destination would have been much greater than it is today.
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.
This is known colloquially as a fat-tailed distribution.
Graphs of very different topology qualify as small-world networks as long as they satisfy the two definitional requirements above.
This follows from the defining property that the mean-shortest path length be small.
Several other properties are often associated with small-world networks.
Similarly, the number of relay stations through which a message must pass was not always small.- helps you find the right local businesses to meet your specific needs.Search results are sorted by a combination of factors to give you a set of choices in response to your search criteria.Tacit assumptions, if not examined, can cause a bias in the literature on graphs in favor of finding small-world networks (an example of the file drawer effect resulting from the publication bias).It is hypothesized by some researchers such as Barabási that the prevalence of small world networks in biological systems may reflect an evolutionary advantage of such an architecture.
Typically there is an over-abundance of hubs – nodes in the network with a high number of connections (known as high degree nodes).