Rarity of Scale-Free Networks in the Real World
https://www.quantamagazine.org/scant-evidence-of-power-laws-found-in-real-world-networks-20180215/
It is a common assumption that most real-world networks can be approximated as scale-free – i.e. the degrees of the nodes in the graph follow a power-law distribution – but how often does this model fit in real life? The article concerns a paper (https://arxiv.org/abs/1801.03400) by Anna Broido and Aaron Clauset which posits that scale-free networks are not as common in the real world as were generally believed in the past. Analyzing a set of 1000 real-world networks, they found that only 4% of them were strongly scale-free (resembling a power-law with exponent between 2 and 3), and only about half of them are even close to scale-free; and even much of that half is not significantly closer to a power-law than to other distributions. There was also variation in this based on the type of network: social networks tend to be farther from scale-freeness than information-based networks, which makes sense when considering that different driving factors affect the structure of different types of networks in various ways. Properties like Triadic Closure in social networks lead to fewer extremely large hub nodes than can be found in networks whose structure is influenced by information cascades – such as those found in technological systems – that tend to lead to a distribution closer to scale-freeness.
Much of the problem with identifying too many types of networks as “scale-free” stems from the imprecision of language as to what exactly the term means, as well as the lack of use of actual statistical techniques. Besides, many network scientists have a physics background and they tend to prefer the scale-free approximation as a rough model, where real network degree distributions could be interpreted as perturbations. This type of approximation is commonly done in physics. Such a perturbative approximation for degree distributions, however, does not seem to hold at all in many real-world examples. In networks where information cascades are involved, “rich-get-richer” phenomena come into play that tend to lead to a power-law distribution of values, and in this case, degrees of nodes in the network. But the wide range of distributions found in various types of networks implies that these effects are not the only dominant factor driving the patterns in real networks, particularly social ones.
As for my view on the matter, I believe that both the physicists’ approach – of applying perturbations to a single model – and the statisticians’ approach – of doing a rigorous analysis of the data to see if it fits some distribution – have merits as regards investigating distributions of degrees of nodes in networks. For a better understanding of real-world networks, in my opinion, other phenomena should be able to be more precisely modeled based on the various network data set, and different kinds of networks could be modeled “physically” as a result from the combination of several dominant phenomena in addition to extra perturbations.