Those are found interatively by the following algorithm.

So there's a fair amount of interconnection between a node's neighbors.

So just getting it correct to a couple of digits is probably sufficient.

Cluster ordered dither

So we'd like to have a way of getting a pretty good answer in time a lot less than this.

And the answer is 2.

And if you do that, you end up with K minus one clusters instead of k clusters.

Next I want to focus for a little while on the notion of a clustering coefficient.

I am going to say that the clustering coefficient for graph is just the average of the clustering coefficients of the nodes in the graph.

I actually have some friends who work on this too.

Suppose we're given the following data points in a 2 dimensional space.

Suppose you are given data like this, and you wish to learn that there's 2 clusters a cluster over here and a cluster over here.

And second, to narrow this down, it feels that there are clusters of data the way I do it.

K Means is an iterative algorithm and it does two things.

C6 equals to and similarly well c10 equals, too, right?

Comparing its brightness to brightness of cepheids in our galaxy, immediately told us that Andromeda is much, much further away than anything in our galaxy.

let's go through how this is often defined.

The moons of Saturn and Jupiter.

All the data points on the left correspond to the red cluster, and the ones on the right to the green cluster.

So as a concrete example, let's say that one of my cluster centroids, let's say cluster centroid two, has training examples, you know, 1, 5, 6, and 10 assigned to it.

Jupiter's Moons...

The last question asked, what is the maximum clustering coefficient for a node in B?

I'm going to do. The first step is to randomly initialize two points, called the cluster centroids.

Next is lower case k.

And so in the earlier diagram, the cluster centroids corresponded to the

Jupiter Moons Tool

It orbits with such planets as... Venus, Saturn, Mars, Jupiter

K means estimates for a fixed number of k. Here k 2.

So the optimal cluster center would be the halfway point in the middle.

It's likely somewhere over here where I drew the red dot.

So, let me do that now.

Planet of the Apes.

Another star system. Another planet.

K means is a very simple almost binary algorithm that allows you to find cluster centers.

If we use k means, we shouldn't increase the number of cluster centers.

Jupiter, Mars, Saturn, Venus...

So just to remind you, here's some code for computing the clustering coefficient of a graph with respect to a particular node v.

Suppose we are giving you 4 data points, as indicated by those circles.

I'm going to color them either red or blue.

It is not the perfectly flat system like the disk of the Milky Way, but it is flat.

Order them from the lowest clustering coefficient to the highest clustering coefficient.

Who formatted this thing? And they used clusters instead of physical sectors for allocations,

There stand some interesting places a little further out the moons of Jupiter and Saturn.

For this problem we have 6 graphs, and we want you to order them with a clustering coefficient of the red node of each graph.

Particularly, there's a place called Europa, which is