Random Network Connectivity Can Be Delayed, But With Explosive Results, New Study Fin

[Kernel]

A trio of mathematicians studying random networks has provided new evidence that connectivity can be appreciably delayed, but only at a cost. When it finally occurs, the transition is virtually instantaneous, like a film of water abruptly crystallizing into ice.

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[WingedPanther]

I'm not sure which is stranger, that somebody actually studied this (the results seem pretty intuitive to me), or the fact the results are a "big deal".

[Jordan]

In the life of many successful networks, the connections between elements increase over time

I read the whole thing and it seems like this first sentence is the sum of the entire article, which seems like common sense.

[WingedPanther]

It's a little more complicated than that. The real key is towards the end of the article. If you pick the connections at random (assume no double connections), then the size of each connected set of node will grow in a more or less linear rate at the beginning, and accelerate slowly as the nodes start to hook into each other.

Consider a set of 64 nodes:
By random activity, the average number of nodes per group after 32 links would be around 2 with around 32 groups. After 64 links, you would start getting loops within groups, so you might be at 3 and 24 groups. and after 96 links you might be at 4.5 and 16 groups.

However, with the suppression approach, it might grow more like 2&32, 2.5&28, 3&24. What's happening is the nodes are encouraged to not join each other, but instead form internal loops. However, what happens is that the internal loops will result in an unsustainable situation where they will suddenly not have much left in the way of internal loops to form, so the small groups will suddenly start merging at a later time than normal.