Now, that we've learned the two concepts
of node degree and connected components,
we can start to apply them immediately to
the dining-table's partner data set and
see what insights we can get out of it.
First, let's look at degree.
Now we have some choices.
This is a directed network, so we can look
at InDegree, OutDegree, or just undirected
degree.
Now, why doesn't OutDegree make sense?
Well, every girl is naming two other girls
as their as her first and second choice.
Therefore, all the nodes are going to have
the same degree.
Same OutDegree.
So we don't want OutDegree.
Indegree, on the other hand, is a lot more
interesting, because it's a reflection of
popularity.
If lots of other girls want to sit with
you at the same table, well, that says
something about how desirable you are in
this girl storm.
So let's look at that.
The degree is calculated automatically, so
you can just go straight to Ranking >
Nodes > InDegree.
Now, we could color the nodes by InDegree,
but we're going to save color for the
connected components.
So let's instead look at size, it's this
little diamond shape here, so I'm going to
click on it.
And we can chose the Min and Max size.
I'm going to go since these nodes are
sized 5.
I'm going to set the Min size a little bit
lower at 2 and the Max size maybe twice
that.
There is this option called Spline.
And this just says, how does this size
vary as this quantity of interest varies
in this case in degrees?
Since the inequality in popularity isn't
that large and it's a relatively small
network, this linear relationship is okay.
However, if for example, you were looking
at a massive network a directed one such
as the web.
And, well, you wouldn't be looking at the
whole web, but say a subset of the web.
And there could be one page that has
100,000 in links, and many other pages
that have one in-link or no in-links.
And you wouldn't want a node that's
100,000 times bigger than other nodes.
It would just obscure your whole
visualizations.
In that case, you may want to do something
like a law of linear relationship,
something like this.
But for our purposes here, we're just
going to go linear.
So, let's apply that, and voila.
Instantly, we can see that some girls are
more popular than others.
Marion and Eva look like they're most
popular and Hilda Doesn't seem to be doing
too poorly either.
Now this is all visual.
And if we want to actually look up the
numbers.
What is the InDegree of each node?
If we simply go to Data Laboratory.
Unfortunately, it doesn't populate the
degree automatically.
So we're going to go back to Overview.
And we're going to ask it to calculate the
Average degree.
Now, the Average degree is 2, which we
sort of knew, because we have 52 edges and
2, 26 nodes, so you can divide 1 by the
other.
So nothing surprising there.
It has given us the Degree Distribution.
We're actually interested in the In-Degree
distribution.
And here, you can see that, for example,
two girls have In-Degree 6, but I don't
know, nine girls have In-Degree 2.
So that's interesting in and of itself.
However, what is super nice about this is
that we can go back to Data Lab.
And now, we actually have the In-Degree
and clicking on top here of this sorts
lowest to highest.
Let's click again and we have the two
girls who have In-Degree 6 who are Marion
and Eva.
So that's a nice way of just getting at
the, numbers.
And, also, if you're interested in the
Debris Distribution you can have a quick
look like this.
Of course, you can export this spreadsheet
and analyze it further as well.
So back to the Overview.
What we have is a picture where some girls
are more popular than others, but we don't
really know whether there certain cliques
or how information might flow.
So, I'm going to start out by asking a
question, you now, if someone had some
piece of gossip, one particular girl.
Where could that gossip go?
Or if you had a set of girls, would they
all be able to hear gossip from everyone
else?
And this is precisely the question of who
is in the same strongly connected
component, because if you're in the same
strongly connected component with someone
else, it means that anything that they
find out can potentially make its way to
you.
So let's find the strongly connected
components.
I'm going to go back to the Statistics
tab.
If you have Filters instead, just make
sure you click on Statistics.
And I'm going to click on Connected
Components.
I'm going to say Run.
And it's going to ask me if I want the
strongly connected components.
Which I can get in a Directed graph, or
not.
Yes, I do in fact want the strongly
connected components.
Because, if you imagine the flow of
information, if one girl says she would
like to sit with someone else, but that
one, that person doesn't want to sit with
her.
Well, they may also not be willing to
share information with her.
So, we really want to take into account
the directionality of the edges.
So I'm going to say, okay.
And, it's telling me there is one weakly
connected component, which just means if
we treat the edges as undirected, everyone
is connected directly or undirectly, which
is true.
But we just have a single connected
network but it's telling me that there are
actually 11 different strongly connected
components, meaning that information
wouldn't circulate throughout the network
following directed edges.
So, we're going to close this, and now,
let's color the nodes by the strongly
connected components.
So, I'm going to go to Partition here, and
I want to partition the Nodes, and I'm
going to click Refresh to just get this
new partition.
Which should be the Strongly-Connected ID.
And, it's giving me some colors some of
these seem a little bit similar, so let me
just see.
I'm going to right-click and say Randomize
colors and these look a little bit
different.
So I'm going to Apply them.
And I think this paints a very, very clear
picture about the dynamics in this in this
among this group of girls.
So first of all we have the purple cluster
here, where all of these girls may be
sharing information with each other and
they also include these two very popular
girls, Marion and Eva.
You see this one girl here, Alice, who
names two girls in this cluster, but her
color is actually different.
She's in the strongly connected component
all by herself because, actually, no one
selected Alice as someone they wanted to
sit with.
We see, this little component here of
three nodes in blue, Betty, Hilda and
Hazel.
All had, well, Hazel had selected Hilda
and vice versa, and Betty had selected
Hilda and vice versa.
So they form one strongly connected
component a similar dynamic with Jane,
Mary, and Edna.
And here is an example with Helen, Jean,
and Robin.
So here, you actually have a closed triad,
but what has happened is that Helen and
Jean mutually chose each other.
And then, Jean chose Robin as her second
choice.
And then, Robin chose Helen.
So you can kind of circulate in here.
And then, Ada and Cora are their own
strongly connected component, because they
chose each other.
So this shows you a bit of the dynamic of,
of [laugh] girls in, in, you know, earlier
stages of their lives.
But also, there's some recent research
showing that most social networks, when
you're naming friends tend to be fairly
asymmetrical like this, and in this case,
because it's a relatively small network,
etcetera.
Even just looking at the strongly
connected components without applying
community detection algorithms, which is
something that we're going to be doing
later on.
We can figure out a lot of the dynamic
between the girls.