If you look at any node in the left side say the middle one.

Let's consider the complete graph, also known as a clique on n nodes.

I wrote a little piece of code to actually generate a complete graph and then return the number of edges in that graph.

So given a node v or computing the clustering coefficient involves

We start off by generating a set of n nodes with no edges at all.

We perform alpha beta pruning.

With that as our insight, can we actually write down what the formula is for a graph with n nodes?

There's node 0, node 1, node 2, node 3, and node 4.

However many nodes it marked, we're going to add that to the total number marked.

This is just where we are.

This one is being expanded first. It's being removed from the queue.

F and G and itself that it can reach no other nodes by non tree edges and the smallest of those numbers is two.

Like before I've got this make_link function, and I'm going to make an empty graph with 256 nodes which is going to be arranged a grid a number nodes per row and column on a side here is the square root of n or 16.

But let's take a look at the running time given that we can do this distance reduction operation in logarithmic time.

In the star network the description is that there is a center node to which all other nodes are connected using the edge.

But notice that's as far as it goes.

Another possibility is that the answer is yes, all such graphs do.

We just have an empty data structure.

Then we go through its neighbors.

Now, given that we can execute a shortest path from any given node, then m logn time.

As we discussed in the previous Unit, to find the most central node in a social network, it's useful to be able to take each node in a graph and find out how far it is from all the other nodes in the graph to get a square for a particular node and then to repeat that operation essentially to find out the distance from every other node to every other node.

There's really two little blocks of things that are going on.

We can add this edge, and are there any more edges we can add while still being able to draw it in a plane?

In this example, Javier was our starting node and it had degree 3.

Then what we're going to do is we're going to count up the number of links between these neighboring nodes.

It's configurable, but in our case, we're using a replication factor of 3, which means that if a piece of data lives on this node, it is also on this one and this one and that happens all around the ring.

Here's kind of a formula for the clustering coefficient.

I'll give you an algorithm for solving 4 colorability.

We choose half the nodes at random in this graph to be S2.

When this is all over, when this loop is done, we have the D⁰n, but D⁰ n,i,j is the length of the shortest from I to J only hopping on nodes that are numbered less than n, but that's all the nodes.

So, we take the distance from the start to where we are now.

What we're going to do is we're going to connect edges up in a particular way.

And it can actually be all the way to one if we have a cleek.

We go back up and handle the next node closest to the start state.

So the running time of Dijkstra in terms of n and M and here's a sketch of the algorithm again.

I used numbers here, because it was really easy to do.

We have a max node. The two actions A and B.

We're going to average it for the n nodes in the graph.

So, following sort of a naive kind of algorithm design, well, this should work and it's not so terrible.

So we give it a single source. We give it a single node in the network.

A leading 0 doesn't change anything, but this second hypercube everyone is going to get a one out in front. Again, thinking about your binary numbers, what is that doing?

By this reasoning, we can see that it would take at least seven edges needed to make B have a single reachable component consisting of all the nodes.

So let's do this.

Here's the sketch of the algorithm again.

In the alarm network we saw previously, we took care to make sure that we had all the independence relations represented in the structure of the network.