The Friendship Paradox

The Friendship Paradox

Do you think you’re cool? Sociable? Extroverted? Do you consider yourself more popular than your friends? Well, the Friendship Paradox says otherwise. You aren’t as popular as you thought you were…

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The Friendship Paradox states that your friends have more friends than you do. It sounds like a pretty bold statement, I know. But it’s probably true for most people – just look at the mathematical proofs here.

But if you’re too lazy/busy to click on the link, I’ll give you the gist of it.

First, let’s look at research. Exhibit A: Facebook. The average Facebook user has 245 friends, but the average friend on Facebook has 359 friends. Exhibit B: Twitter. Research shows that both the people that a Twitter user follows and the people that follow him have more followers than he does. Also, on average, a Twitter user tweets fewer times than the mean number of times that his followers tweet per day.

Second, think about this: Why do we become friends with certain people? Well, it’s probably because those people are, in general, very outgoing. You tend to be friends with popular people. There are two kinds of people – those with a few friends, and those with a LOT of them. There are much lesser people in the second category. However, because these people have so many friends, chances are, you’re friends with them too. These people raise the average number of friends that your friends have, so you have less friends than your friends have.tumblr_n54a23srx91sszkooo1_500

Now, take a look at the picture above. Notice how, as you look farther outward from the center, the number of people appears to be growing. This is because you are adding the friends of your friends, of your friends, of your friends, and so on.

Anyway, the point of that was to show you that the friendship paradox can be used in epidemiology (the study of diseases, including their transmission and effects). If you have a disease and you come into contact with your friend, the disease will be spread to him. Then that friend will spread it to his friends, who will spread it to their friends… Pretty soon, we have an epidemic on our hands. I’m exaggerating, of course, but now I think you get the point.

Well, that’s all for this post. But before I go, let me give you some genuine (and slightly cheesy) advice: when it comes to friends, quantity doesn’t matter so much as quality. True friends are much better, and much more rare, than fake ones. So don’t be sad if your friends have more friends than you.

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Sources:

  • Metro.co.uk, Ellen Scott for. “JSYK, All of Your Friends Have More Friends than You.” Metro. N.p., 21 May 2016. Web. 23 May 2017.
  • “Friendship Paradox.” Wikipedia. Wikimedia Foundation, 11 Apr. 2017. Web. 23 May 2017.
  • ArXiv, Emerging Technology from the. “How the Friendship Paradox Makes Your Friends Better Than You Are.” MIT Technology Review. MIT Technology Review, 19 Sept. 2014. Web. 23 May 2017.
  • “Why Are Your Friends More Popular than You?” The Economist. The Economist Newspaper. Web. 23 May 2017.
  • “Networks.” The Friendship Paradox – Why Your Friends Have More Friends than You Do : Networks Course Blog for INFO 2040/CS 2850/Econ 2040/SOC 2090. N.p., n.d. Web. 23 May 2017.
  • “Why Your Friends Have More Friends than You: The Friendship Paradox.” Mind Your Decisions. N.p., 25 Aug. 2012. Web. 23 May 2017.
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14 thoughts on “The Friendship Paradox

  1. Ananya,
    Wow. At first I was really confused about how this whole friendship thing worked, but after you explained it, it made a lot of sense. This is super cool to think about, and the more I do think about it, the more it makes sense.

    Like

    1. Thanks for commenting! I agree with you. When I first learned about this paradox, it was pretty weird, but after reading some examples, it became clear. I love paradoxes because they make sense, and yet they’re impossible, in a way. They’re so self-contradictory. I hope you enjoyed reading this post, and I look forward to seeing you in my future posts!

      Like

  2. Dear Ananya,
    This is a really eye-opening concept that I have never heard of before. I think this is a really interesting take on friendship. Your blog is really well written, and I really enjoy your choice of graphics. The pictures you used in this post make me continue reading the post, and really connect back to your post. Thank you and keep writing!
    Abirami

    Like

    1. I think this theorem teaches people not only math, but also important life lessons. Thanks for the compliments! I tried to add funny pictures and relate them back to the content. I guess it worked! Anyway, thanks for commenting, and I hope to see you in my future posts!

      Like

  3. Hi Ananya!
    I really appreciate your disclaimer in the end of your post, because I have to admit, the beginning really got me in my emotions. Also, the pictures you added to your post really enhanced the comical effect it produced, and helped me engage with it better. Hope to see more posts from you soon!

    Like

    1. Thanks, Tausiful, for reading and commenting! I hope I didn’t hurt your feelings while explaining this paradox; that’s why I added that last paragraph. I’m glad you found it funny and engaging, though! I hope you read my future posts!
      – Ananya G

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  4. I’m quite impressed with this post. I have always wondered how I stand socially against my friends and now I have an idea. What I don”t understand is if hypothetically speaking, 2 friends are sitting here and reading this blog. According to this post, the other friend has more friends than the one reading the post. That means both friends have more friends than their counterpart, but that doesn’t make sense. Only one friend can have more friends, right? Anyway, as you suggested, maybe I should just focus on the quality of my friends, instead of the number. I look forward to future posts.

    Like

    1. I’m happy that you’re “quite impressed with this post”! In response to your question, the friendship paradox says that the average number of friends that your friends have (all your friends, not just the one sitting next to you) is higher than the number of friends that you have. Therefore, in that situation, one person would have more friends than the other, unless they have an equal number of friends – but that’s unlikely. Anyway, I hope that answers your question (and makes sense). But yeah, quality matter more than quantity when it comes to friends. Thanks for reading and commenting! I hope you read (and maybe even comment on) my next post!

      Like

  5. Dear Ananya,
    I’m really impressed with your blog and posts because sometimes just simple math makes my head explode. I think this paradox is very interesting because I’ve never heard of it before and it makes complete sense. However, that doesn’t mean I don’t have trouble wrapping my brain around it. The twitter and facebook thing kinda through me for a loop because even though I understand that it works it still boggles my mind on how it works. I enjoyed reading your post!

    Like

    1. I totally understand, because I felt the same way at first. Like it makes sense to me, but at the same time, it doesn’t… Hmmm. That’s paradoxes for you, and that’s why I love them so much. Anyway, thanks for the feedback, and I hope to see you soon (in my next post)!

      Like

  6. Hey Ananya! This was a really cool post! I got a little confused when you said “These people raise the average number of friends that your friends have…” because if they become my friends it doesn’t necessarily mean they will be friends of my other friends. Could you explain what you meant? I’ve never actually heard of this before, and I really enjoyed reading your post!

    Like

    1. When I said that, I meant that those people increase the average amount of friends that all of you friends have, combined. It is not necessary that those people are friends with your friends. Does that make sense? I hadn’t heard of it either, before this. It’s amazing, the things you can find when you search up “paradoxes” on the internet. Thanks for commenting! Maybe I’ll see you in one of my future posts!

      Like

  7. Hey, I really liked your logical explanation – it was completely mind-blowing! I really didn’t know that my (well, a random person’s, since I have no friends) than their friends. I also like your graphics!

    Like

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