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.