After the Cylon Holocaust, how many people would know each other? If you are not familiar, in the show Battlestar Galactica (2003) the Twelve Colonies (planets) are wiped out by the Cylons which they created. Only about 50,000 humans survive in the form of a rag-tag fleet of civilian ships and one Battlestar (give or take).
There are at least a few instances in the show of people who were not on the same ship who are re-united or at least know each other from before the attack. Considering that -99.9998% of the human population was wiped out I feel like this would be unlikely, but I want to know exactly how unlikely.
Of course, I am not concerned with celebrities and notorious individuals who were "known" by a large number of people. I am interested in personal connections. Obviously the definition of "knowing" someone is fuzzy, but at least one study, cited in the New York Times, estimates that the Average American knows 600 people. In reality I suspect the real number could be significantly different, but this seems like a realistic ballpark number of people for which the average American could put a name to a face. I'd even be willing to round it up to a generous 1000 personal connections. American society seems like a good proxy for the societies of the Twelve Colonies.
According to Wikipedia, there were about 28 billion people alive before the Cylons attacked. So we have all the numbers we need: 28 billion to start with, culled down to 50,000. Average connections of, say, 1000, generously speaking.
To abstract and simplify the situation a little, why don't we just imagine that people everywhere died at random, ignoring the fact that survivors were clumped on ships. I am not interested in the intra-ship relationships anyway. I can calculate that the average person would know about 0.0018 people after the attack. What I don't know how to figure out is how many surviving connections between people there would be in a population of 50,000. And that is the real question. It's not just 0.0018 × 50,000, right?
I can't figure out the logic, but I don't expect this to be too hard for some math major to solve. Once you figure out the formula then we could see how likely it would be for you to know people in various social circles, like say 50 for close friends, family, and work colleagues.
Bonus question: would the fact that survivors were grouped into ships have a significant effect on the likelihood of intership connections?
 A: One way to go about it is to estimate the probability that two randomly selected individuals know one another. Ignoring all socially induced effects (you tend to meet your friends'friends, etc.), suppose this probability is $p$. Given that the pre-cylon population size is 28Bs, the expected number of people one would know is $28\, 10^9\times p$. I order for this to be, as you suggest, 600, you need 
$$
28\, 10^9\times p=600\rightarrow p=\frac3{140\,000\,000}.
$$
With a remaining population of $50\,000$, the number of possible pairs is $$
k=\frac{50000\times49999}{2}=1\,249\,975\,000
$$
All in all, the expected number of surviving connections would be
$$
1\,249\,975\,000\times p = 1\,249\,975\,000\times \frac3{140\,000\,000}\approx 26,78.
$$
Inter-ship? Well, suppose there are, say, 1000 people on each ship. Given 2 ships, $1000\times999/2$ pairs are possible, each with a probability $p$. Assuming independence, the probability of no inter-ship relation is
$$
(1-p)^{1000\times999/2}\approx 0,989354.
$$
Therefore the probability of someone on ship 1 knowing someone on ship 2 is $1-0,989354\approx 1.06~\%$.
A: This question is old, but I think you're working with the wrong constraints.
If there's 28 billion people over 12 planets, most of the population of each planet is irrelevant because they probably never leave their planet.
Even today, only about 4% of humans are travelling internationally by plane, and 1% of people account for half of all airplane emissions.
https://partner.sciencenorway.no/climate-change-global-warming-transport/1-of-people-cause-half-of-global-aviation-emissions-most-people-in-fact-never-fly/1773607
We don't have any evidence of how many people travel interplanetarily, but at a guess, at least half of that 50,000 are those 'super frequent' fliers, whether that's 1% or even less of the global population, same as today. This is reflected in the show by a disproportionate number of politicians and ppl in military, reporters, and finally people who work in space travel.
I'm not even breaking the numbers down here, but yeah, given those shared environments, they would be hugely likely to know each other.
Can't work out the proportions without estimates of interplanetary travellers in this universe.
1% of 28 billion is 280,000,000
Counterintuitively, the less people that were travelling in space when the cylons attacked, would actually indicate that it's even more likely that these people who survived, all associate or work in the same social circles, because that says most of the population never leave their planet, and these people are essentially super travellers, and super connected.
