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Education 880 views 8 likes 0 dislikes 02 Jun 2012

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[Narrator] Here's a typical group of friends in middle school, and some of the people are popular, some of them might not be.

so here's a typical group of friends in middle school and some of the people are

The first step to deciding who's popular is looking at who has a lot of friends.

popular some of them might not be the first step to deciding who's popular is

Let's draw in some links that show who's a friend,

looking at who has a lot of friends so let's draw in some links that show who's

and friendship links are one directional,

a friend and friendship with links are one directional just because alice's

just because Alice is friends with Bob doesn't mean that Bob is friends with Alice.

friends with Bob doesn't mean that Bob is friends with Alice so we'll draw our

We'll draw our links as arrows so this means this person, we'll call him Bob,

links as arrows so this means this person will call him Bob his friends

is friends with Alice, and let's say Alice has many friends,

with Alice and let's say Alice has many

and let's say Bob is also friends with this person.

friends and let's say Bob is also friends with this person they're friends

They're friends with each other.

with each other we have lots of

We have lots of friendship links, some of them are bidirectional but not all of them.

friendship links some of them are bi-directional but not all of them so we

We have lots of friendships.

have lots of friendships so is this

Is this enough to decide who's popular?

enough to decide who's popular so if you

If you went to a school like I did it's not.

went to a school like I did it's not

Just having a lot of friends is not enough to make you popular.

just having a lot of friends is not enough to make you popular you have to

You have to have the right friends.

have the right friends you have to be

You have to be friends with the popular people.

friends with the popular people so it's

It's not enough to have lots of geeky friends say in high school.

not enough to have lots of geeky friends

You've got to have lots of friends that are popular.

say in high school you've got to have lots of friends that are popular so that

That means the definition of popular isn't just about having lots of friends.

means that the definition of popular isn't just about having lots of friends

It's about having lots of friends who also have lots of friends.

it's about having lots of friends who

That's what makes someone popular.

also have lots of friends that's what

We could define popularity of a person is the number of people who are friends with the P.

makes someone popular so we could define popularity of a person is the number of people who are friends with P this means

This means the number of links from someone else to that person is their popularity score.

the number of links from someone else to that person is their popularity score so

Here is Charlie. There are 1, 2, 3 links into Charlie, so Charlie's popularity score would be 3.

here's Charlie so there are 1 2 3 links into Charlie so Charlie's popularity score would be 3 Alice also has three

Alice also has 3 links, so her popularity score would also be 3.

links so her popularity score would also

Bob only has 1 arrow going to Bob, so his popularity score would be 1.

be three Bob only has one arrow going to Bob so his popularity score would be one

This isn't a bad way to define popularity, but it's not quite right.

so this isn't a bad way to define popularity but it's not quite right so

The definition of popularity doesn't just depend on the number of friends you have.

the definition of popularity doesn't just depend on the number of friends you

It depends on both the number and the popularity of your friends.

have it depends on both the number and the popularity of your friends so we can

We can change the definition; let's instead define the popularity score of a person T.

change the definition let's instead define the popularity score of a person

Now it's going to be the sum of the popularity of all their friends.

T now it's going to be the sum of the popularity of all their friends

We can write that in a mathematical way, so using the sigma means to sum up.

so we can write that in a mathematical way so using the Sigma means to sum up

We're going to take each friend that is in the friends of P,

we're going to take each friend that is in the friends of P and we're going to

and we're going to sum up the popularity score of the friends.

sum up the popularity score of the

If the mathematical notation is unfamiliar to you,

friends if the mathematical notation is

we could also write this as pseudo-Python code.

unfamiliar to you we could also write this as pseudo Python code we're

We're thinking of the popularity of a person P.

thinking of the popularity of a person p

Let's assume we have a function that gives us the friends so we're going to start with a score of 0.

let's assume we have a function that gives us the friends so we're going to start with the score is zero we're going

We're going to loop through the friends, and for each friend,

to loop through the friends and for each

we're going to add to P's score the popularity score of the friend,

friend we're going to add to peace corps the popularity score of the friend and

and we'll return the score as the result.

will return the score as the result so

Now you've seen a mathematical definition of popularity.

now you've seen a mathematical

You've seen the same thing as code.

definition of popularity you've seen the

I'm going to ask you a very important quiz question next.

same thing as code I'm going to ask you a very important quiz question next it's

It's an easy one to get right if you try twice because there's only 2 answers,

an easy one to get right if you try twice because there's only two answers

but think about it carefully, see if you can get it right the first time.

but think about it carefully see if you can get it right the first time

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