PubMed · 1055851
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K K Jung. 1975-04-25. [Human relationships].. https://pubmed.ncbi.nlm.nih.gov/1055851/
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How do we make acquaintances? A simple observation from everyday experience is that often one of our acquaintances introduces us to one of his or her acquaintances. Such a simple triangle interaction may be viewed as the basis of the evolution of many social networks. Here, it is demonstrated that this assumption is sufficient to reproduce major nontrivial features of social networks: short path length, high clustering, and scale-free or exponential link distributions.
We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: (a) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; (b) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and (c) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.
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