I don’t know anything about these network models, [This](https://youtu.be/RfgjHoVCZwU) video sparked a few questions in my mind!
In: 8
The basic idea of randomness is that no particular choice is favored, for any reason, over the alternatives. Pure chaos. We use this idea of behavior to model “ideal” systems, systems that are as simplistic as can be envisaged. No filters that favor one set of results over other sets. The idea of randomness means that, everything that can happen, will happen, as long as the data set is large enough. No particular specific sequence of results will occur more often than any other equally likely specific outcome.
For example, the standard idea of coin flips can be considered. When a series of outcomes is considered, even random systems will result in some outcomes happening more often than others. This is generally because some outcomes, like say, 3 heads and 3 tails, can happen multiple ways while others, like say 6 heads, can only happen in a single way. Some outcomes, because they have many possible ways to happen, tend to happen more often than other outcomes which can only happen under a few to maybe even only one possible way. Although a particular sequence Head-Head-Head-Tail-Tail-Tail is only as likely as any other specific sequence, the result of three heads and three tails can arise from numerous different sequences. If six such possible sequences exist (there are truly way more), that 3H-3T outcome would be six times more likely than one of its specific paths, or even more importantly, some result that can happen by only one specific path.
When you perform enough trials, the outcomes that can happen by more different ways will happen more frequently. So, while no one particular path is favored over any other path, the overall outcome can be seen to have some results that are more likely than others.
Thus, the basic idea is that while randomness does not dictate anything about a particular specific outcome, when performed repeatedly, some general outcomes will dominate. More ways to happen so happen more times. This set of higher-occurring outcomes tends to be what we call “average”. When graphed on a frequency diagram, you will see a “normal” curve, one that is symmetric around the most common outcome (the mean, “average” outcome) with decreasing frequency toward the fringe outcomes.
This is how randomness becomes “predictable”. We can predict, fairly closely to what will happen, what results from a series of trials will result. We can predict how likely (how frequently) someone will get a full house playing poker, and explain why two of a kind hands are way more common than four of a kind hands.
The flip side of this idea is that we can tell when something other than randomness is at work too. The results that happen will turn out to be different, after enough trials (tests), from what would be expected if randomness was the only thing happening. These factors are actually the interesting things to examine, from a scientific view. They tell us how the world, even though random at its base, can develop complexity (which would not happen in any regular way in a totally random system). It could happen once, because everything can happen once (more or less), but when it happens, again and again, way more than it ought to just from randomness, then clearly something else is happening that we need to understand.
In this particular video, the idea of random network formation, that any node could, by random results, end up being the most common, is found to be wrong in actual systems. Actual systems have a selection bias, in a way. What is that selection bias and why does it affect the outcome, is the interesting thing. It turns out that lots of extremely complex systems can form even if there is really only random choice, with a small selection bias, at work. In the idea of the WWW, the bias is, in part, simply how long the node has existed. Older nodes will have more connections. They will tend to connect to added nodes through existing connections rather than making a new direct connection though. The results are not what randomness would predict.
With networks, there are many other biases that can affect outcome, like some sites are simply more desirable to the human user than other sites, so more links will develop in that direction.
This is, at least, how I understand the points made in that video. I hope this helps. I tried to keep it simple.
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