Friends of Friends

Probability Level 1

Here is a network graph constructed with data from Facebook of 20 people and all of the mutual friendship connections among them. Clearly Barbie has the most friends to invite to her parties (9), but if invitations go out not only to friends but also to all friends of friends, then whose party will have the most invites?

Notes and assumptions

  • Each dot represents a person.
  • Each line represents mutual friendship between the people on either end .
Devon Barbie Dude Diva Ken

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Chung Kevin by Chung Kevin , 45, Australia

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3 solutions

Chung Kevin
Oct 16, 2015

Dude may only have 3 friends himself, but his friends are very well connected. Dude is either Friends or Friends of Friends with everyone except Diva, and Devon.

9 Helpful 0 Interesting 0 Brilliant 0 Confused

Dude is friends of friends with Ken through Barbie

Christine Derby - 5 years, 7 months ago

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Oh yes. I've edited the solution.

Chung Kevin - 4 years, 8 months ago

I think that the corect answer is : All of them will have the same amount of invites.

Dennis Moru - 4 years, 8 months ago

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Not true. Devon can only invite 7 people.

Chung Kevin - 4 years, 8 months ago
Saya Suka
Mar 24, 2021
Name Number of friends Number of friends of friends not already friended Total guests invited
Barbie 9 4 13
Ken 4 7 11
Diva 4 3 7
Devon 3 3 6
Dude 3 14 17

Answer : Dude is the most well-connected-to-the-second-degree person in their circle with 17 total invites.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Renemar Sultones
Apr 10, 2018

The only people who's not getting invitation from Dude would be Devon, Ken and Diva. For Barbie: Devon and 5 people ....

Dude would have the most invites since only 3 people are not getting invited from his connection.

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Ken gets an invite from Dude through Barbie

Gioele Ciaparrone - 3 years, 2 months ago

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you're right, i missed the the connection between Barbie and Dude. so only 2 friends not getting the invite.Thanks.

Renemar Sultones - 3 years, 1 month ago

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