When generating random social network using Watts Strogatz (Small World) model or Barabasi Albert (Preferential Attachment) model. What model configuration do you think the best mimicking real online social network such as Facebook or Twitter ?
https://en.wikipedia.org/wiki/Watts_and_Strogatz_model
https://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model
Both the models have their pros and cons depending on the properties of social networks one is interested in e.g. growth, degree distribution, clustering, etc. Each of these models has its limitations and should not be regarded to be fully realistic. One may, however, study the amount of deviations in the properties governed by a model and those obtained from a real online social network.
you need to look for a measurment study paper of facebook. There you will find values you are looking for. For example, avg degree, cluster coefficient, diameter and separation between nodes (shortest path). These values can be used to generate a new graph to mimic facebook.
start from here,https://research.facebook.com/blog/three-and-a-half-degrees-of-separation/ you will find the shortest path and graph diameter of facebook. you need average degree, https://www.facebook.com/notes/facebook-data-science/anatomy-of-facebook/10150388519243859/. 100 freinds and so on.
It is easy to find the rest
I don't think there's any configuration of these two models that does a good job, so why limit yourself? Both have completely obvious limitations that make the generated graphs significantly and qualitatively different from what you would observe in real social networks. The state of the art is further than that. Have a look at generators like LFR, BTER, or ReCoN (see attached publication).
Article Generating Scaled Replicas of Real-World Complex Networks
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