A small-world network combines elevated local clustering coefficients with mean graph distance comparable to a chosen reference ensemble of random graphs. Both the reference ensemble and the clustering convention must be specified. A network can have these properties without having a power-law degree distribution.
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A small-world network is a type of graph in which most nodes are not directly connected to one another but can be reached from every other node through a small number of connections. This concept was popularized by psychologist Stanley Milgram in the 1960s through his "six degrees of separation" experiment, which suggested that any two people in the world could be connected through a chain of acquaintances involving, on average, just six intermediaries.