Friends of friends of friends calculation?

3ee3ee3ee

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Apr 5, 2020
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So my question is probably very simple but I'm not sure exactly who to ask or how. I want to know how many contacts are generated between people on social media.

For ease of operation I'm going to just say, Facebook.
And let's just pretend a profile has 100 friends and each of their friends has 100 friends with 100 friends each.
I would like to know how many friends of friends of friends etc. The average person has.

I'm asking this because I personally have over 100 friends but under 300 on Facebook. I don't have any random strangers as friends. Of my let's say 100 friends, I have not heard of anyone who knows anyone who has contracted the corona virus. When I was at the store today I was in line 6 ft behind the woman in front of me and 6 ft in front of the couple behind me. Each of them chimed in when I said I didn't know of anybody personally who contacted the virus. All three of them replied concurring that they as well knew nobody nor knew of anyone personally.
The lines of people to the left and right of us overheard the conversation and at 6 ft apart 6 couples and 9 single people all agreed that they knew nobody nor knew of anybody of their friends or friends of friends or friends of friends of friends who have contracted the Corona virus.

That's 21 people collectively who all agreed that they knew no one and knew of no one in any way personally connected to them who has contracted the Corona virus.

I feel like there should be statistically at least one person who knows someone somewhere in the world who has this virus or someone who knows someone who does in a group of nearly 30 people and all of their social connections.

Long question short, I would really like to know how to do the math for this. An answer would be great but the equation would be interesting to have for more than just myself.

Please let me know if you can help me figure out how to figure this out.

Thanks intelligent people!
 
Let the probability of getting the coronavirus in the city you were in be p.

Then the probability of 0 out of k people having the virus is p^k.

You decide on what k and p are. Remember that k is the friends of friends of....
 
I'll give an example.

My county has about 500 confirmed cases in a population of 750,000, so p = 0.000666. The probability of not having the virus (yet) is 1-p = 0.999333. If a group of 10 people around me had about 100 friends each, the probability that none of those 1000 people have it would be (1-p)^1000, which is about 50%.

If I were in New York City rather than the other end of New York, it would be different.
 
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