Hello everybody.

This unit is a quick look at the 
science of networks,

which is one of the fastest growing 
areas of complex system science.

In this unit, we'll survey 
some of the diverse ways

in which networks can appear

in nature, in society and technology.

We'll look at some of the concepts
that network scientists are using

to understand how networks behave,

how they're structured,

and what kinds of implications

these concepts turn out to have

for many aspects of our own lives.

Let's get started.

Networks are ubiquitous,

and the science of networks

is growing extremely quickly.

Let's look first at some 
examples of networks

in nature and society and technology.

This is a picture of a neural network

of a worm called c. elegans,

a very small worm,

that has only about 300 neurons.

This is a map of all of 
those 300 odd neurons,

Each sphere represents a neuron,

and the links between spheres represent

synaptic or gap junction 
connections between neurons.

So this is a great example of a network.

Every network consists of nodes
and links between nodes.

In this picture, the size of the node
represents the number of connections

that are coming into the node.

You can see something in this picture

that's typical of many networks.

The distribution of links is not uniform.

That means that there are some nodes

that have many, many more 
links coming into them,

or out of them, than other nodes.

Nodes like this one, 
that link to many other nodes,

are often called hubs.

Here's another kind of network.

This is a food web,
in which the nodes are

particular kinds of animals,

species, or animal types,

and one node links to another node

if the second node eats the first node.

If this node, for instance, squirrels,

are prey for foxes,

so squirrels link to foxes.

Again, you see certain kinds of hubs.

Like, in this network,
foxes are a hub.

Many links come into foxes.

Another kind of biological network

is a metabolic network.

In the metabolic process,

each node is a different 
kind of chemical,

and nodes are connected if one
type of chemical produces

a second type of chemical,

through a metabolic 
interaction in the cell.

Again, here you can see
some hubs of the network

that have many, many incoming links.

That is, in this case,
these things are created

by many chemical interactions.

This kind of visualization
of network structure

allows us to see the importance

of different kinds of 
elements of a system.

For instance, a hub

seems to be a very important
part of the system,

one that if it is destroyed,

will end up wreaking havoc on
much of the system.

Perhaps the most familiar kind of network
is a map of airline routes.

Here we have a particular airline,

whose hub is clearly Houston,

one of the hubs,

another hub is Newark,

and you can see that there's 
many cities here,

each node is a city,

and each link means that there is a flight
on this airline between the two cities,

there's many cities that have few 
flights coming out of them,

and some small number of cities
that have many flights

coming out of them,
or into them.

Again, this shows us the 
importance of these hubs,

as people who have done 
a lot of traveling know,

if, for instance, the weather is bad 
at a particular hub,

like Houston,

that will disrupt flights

throughout the entire network.

Here's a network that we all rely on.

This shows the North American internet.

Each one of these nodes is a 
particular set of servers,

and links are direct paths 
between the servers.

You can see that there's
certain hubs in this network.

Again, if certain hubs, 
like say this one,

are targeted, 
or go down for some reason,

the whole internet can be
largely disrupted.

The US power grid,

another example of a network,

in which the nodes are 
power substations,

and the links are high voltage
transmission lines,

between power stations.

In economics, we can have networks,
such as networks of banks.

Each node is a particular bank,

and banks are linked if they have

strong interactions, such as loaning
each other large amounts of money.

This kind of network 
can be disrupted,

as we saw during the 2008 
financial crisis, for example.

We can see that say J. P. Morgan Chase

is a hub here in this network

and if this bank gets disrupted,

the whole network can feel 
the repercussions.

The World Wide Web is a very
familiar network for all of us.

This shows some nodes which are
web pages or web sites,

and links, which represent hyperlinks.

This is one very small part of the network

that actually goes around 
the site Wikipedia,

but you can see here that there's
again this structure of hubs,

that is nodes that have many hyperlinks
coming into or out of them,

and nodes that are not hubs,

that don't have very many links
coming into or out of them.

Social networks, another example.

This is a map of friendship links 
in Facebook.

Within the last 20 years,

a science has grown up around

this interdisciplinary field of networks.

Before this new science came about,

networks were studied
in certain disciplines,

for example, mathematicians studied
networks that they called graphs,

and developed a whole theory,

called graph theory.

Sociologists studied social networks.

Economists studied economic 
and financial networks,

and so on.

But the fields were seen 
as largely separate,

and there was little communication

among the scientists looking at 
their own discipline of networks.

But, within the last 
couple of decades,

people have started looking at 
very general science of networks,

in which they ask,

are there properties that are 
common to all the different

complex networks that we see,

and if so, why have such 
properties arisen?

And finally, would it be 
possible to formulate

a general theory of networks, 
that is to understand

their structure, evolution and dynamics

across all the different 
manifestations of networks.

These are all open questions.

We will in this unit

look briefly at how scientists are trying
to answer such questions.

And just to give you a preview,

let me give you a short list of some of
the proposed common properties.

These are the ones that 
we'll be looking at.

The so-called "small world" property

The idea of "long-tailed" 
degree distributions

which has a special case of 
"scale-free" structure

We'll look at clustering and
community structure in networks.

We'll see how certain kinds of structure
allows networks to be robust

in certain ways, but 
vulnerable in other ways.