As we part, I'd like to congratulate you
for sticking with this course throughout
its eight weeks.
I hope that you have a good sense about
networks.
What I, what I hope you got out of it is
understanding what are the key properties
of empirically observed networks, what are
the processes that shape them that help us
to understand what those empirical numbers
mean, and what implications this has for
various functions that the network is
supposed to be carrying out.
For example, whether it's enabling people
to communicate or to search and, and find
one another,
Or, you know, some of the cool and unusual
applications where the nodes might be
different products in a product space that
different countries participate and
compete in.
At the same time, we've in a sense just
scratched the surface of all of the
wonderful research and learning that you
can do in this area.
One thing that I haven't covered at all
are biological networks and this is one of
the largest application areas with many
fascinating findings, ranging from
understanding how different functions have
evolved to how cells work to I mean, it
just goes on and on.
It's, it's really,
I mean, things like the relationship
between genetics and disease, all of this
now is heavily influenced by our
understanding of how things are networked
together.
Similarly, there's so many other
application areas that we haven't, that
you wouldn't even imagine.
For example, network analysis of space
that architects use to understand which
spaces are going to be conducive to
individuals flowing through, which spaces
are going to allow them to communicate.
Just things of that sort.
We also have not used some of the tools
that are heavily used in some domains.
So, for example, there is a most excellent
book by Mark Newman, who's also faculty at
the University of Michigan, called
Introduction to Networks and, it's really
a tome, it's a, it's a very thick book,
where he shows you how using, you know,
some heavy-duty math and analytics you can
derive many network properties from
knowledge of simple things such as the
degree distribution.
So you can actually derive what the size
of the giant component will be given the
degree distribution of the network, for
example.
It also looks a lot at different
algorithms for detecting community
structure and really grounds such
approaches on, you know, kind of, in a, in
a statistical way where you're looking at
ensembles of many different network
instantiations and looking at whether what
you observe is actually significantly
different from what you would see at
random.
On the economic side of things, Matthew
Jackson, who's faculty at Stanford, has
written an excellent book Social and
Economic Networks,
And things that we really didn't get into
that much are, but that the book covers,
are things like, what strategically, if
you have, if the nodes are self-interested
and maximizing the utility that they get
from the network,
How will the network be wired?
Or if you're playing certain games,
I mean we did this simple cascade model
but what if you were playing prisoner's
dilemma on a network.
.
How does the network topology affect the
outcomes?
.
Then Laszlo Barabasi and his collaborators
are writing more chapters of the wonderful
Network Science Book,
That which is aimed more at, at a beginner
audience. So I think you would you could
probably understand, no matter your, your
background, a great portion of that book.
So other topics that we didn't get to this
time around, include how networks evolve
over time.
So, Gephi actually has some functionality
for visualizing how networks evolve.
But questions that you might be interested
in is,
Does the community structure teach?
Does the network densify that is this will
become denser over time?
You can track centralities,
So are there different nodes that emerge
as being important during different time
periods.
So that's a whole area, which, it's sort
of easy to extrapolate from where we are
now to doing it over time.
But, I'm just sorry, I didn't get a chance
to do that with you this time around.
So,
No, another very fruitful part are these
p-star models where you statistically
determine factors that are affecting
network formations, so rather than saying
oh, okay it's going, it'll, it's going to
have this probability of preferential
attachment,
You're going to actually run an analysis
that's going to extract that from the
observed data.
You know, is the network going
preferentially or not?
Is triadic closure a large factor in how
this network has formed?
And finally, you know, cool and unusual
applications, they're happening every day
all the time,
Whether you want to understand what's
happening in politics,
In, education.
[laugh].
Really, there, there's no limit to where
you can apply, network analysis.
So I do hope you, have found this class
useful and that now you will go forth and
apply social network analysis to whatever
might interest you.
So, thanks for sticking with me through
these weeks.