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So I'll spend a little bit
of time talking about,

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some very important representations.

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So much of our data,
is represented in the hierarchical format.

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And so graphs and

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trees are very often on the most
common ways that we represent data.

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So I think it's valuable for us to talk
just briefly about some of the different

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options that we have for thinking about
representing graph and tree data.

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So the most common way that
we represent data in a graph

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format excuse me, in a tree is something
that we call a node link diagram.

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And a node link diagram really takes
each different node that has children,

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and represents the children
at an indented way.

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So in this particular node linked diagram,
the root of the tree is all the way

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to the left, and each of the different
leaves are shown at the second column and

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the third column, and far right
you'll see all the different leaves.

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Well one of the most common
things I think I'm asked is,

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how do I squeeze more data into my my,
my tree.

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Well one of the ways is
by rather than using

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a single hierarchy and making it flat.

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But we can do here is have a radial
layout, and this radial layout

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allows the same amount of data, excuse me,
a significantly higher amount of data

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to be presented and it's shown in a way
that all of it can be visible at once.

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And this idea of the node
link diagram can also be used

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in this idea that here called thread arcs

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that are used to show networks
that occur over time.

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And so you can show a single note, and
the way that its children propagate.

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This is very interesting
here in thread arc.

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The idea is that this particular
representation is used to show the way

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that a particular conversational
threads are propagating.

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You can see for example on
the conversation in the middle on the left

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that an original conversation has started
and then without comment another one, and

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then another one, and another one.

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And then finally someone
comments on the very last one.

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Whereas if you look at for example,
the one on the top right, the first,

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the original comment, then spawns one,
two, three, four, five comments.

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And then the second comment
has a child unto itself.

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Separately, if you're interested in

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showing not just the relationships.

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So the things that these graphs
are excellent at showing

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is the hierarchical relationship.

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But sometimes the relationship does not
just include one of containment, but

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it also includes one of magnitude.

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So for this particular kind of diagram,

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something here called a tree
map can become very useful.

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So a tree map is also a hierarchical
diagram like the tree, but

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each child node is organized,
according to the area.

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So you can see here in the top left,
that's a node with no children.

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Whereas, go one below it,
that node has three children and

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the one on the bottom has a magnitude
far greater than the two above it.

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So something like this
is occasionally used.

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You might have seen something like this,
for

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example, on a disk defragmenting program.

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Another way that networks are often shown
is something here called a chord diagram.

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And this chord diagram allows you to
actually show relationships and magnitude.

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And so
this one would work by mousing over one of

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the particular edges which
are shown on the outside, and

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the relationships are shown by arcs
connecting each of the nodes and the width

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of the arc is proportional to the
magnitude, the weight of the connection.

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And so you can see here, this particular
diagram shows a hierarchy and

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magnitude at the same time.

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Another way that you might care
to show something like this,

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is something called the Sankey diagram.

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That the Sankey Diagram is
designed to show the magnitude and

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flow through a network at the same time.

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So, this particular diagram shows how
energy is produced and consumed in the UK.

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So, what you can see,
for example, is on top,

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nuclear is the principle producer
of electricity in the UK.

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And if you go, and
you can see that about half way down,

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there is a bar that represents a node
where transportation, excuse me,

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thermal generation is then used,
and, and that is the consumer of

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nuclear power, and that is then passed
on to the right to downstream consumers.

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So what you can do is you can see how,
for example, things like oil imports and

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oil reserves on the bottom left

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are then passed into liquid
form to various refineries.

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And you can see the magnitude
of the bar here,

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excuse me the height of the bar represents
the magnitude of the relationship.

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So you can see that there's a number of
ways that one could take the same data,

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that is included in a graph structure and
it choose to

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highlight hierarchy, time, and magnitude.

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And depending on how you would choose
to differently represent them,

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if you want to show hierarchy and
magnitude, then the tree map is for you.

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If you want to show time and hierarchy,
then think about a thread arc.

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If you want to show a deep number
of hierarchical relationships,

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then think about the node link diagram.

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And if you're interested
in showing hierarchy and

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magnitude, think about the core diagram.

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And if you're interested
in showing magnitude and

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time, then think about a Sankey diagram.

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But each of this different
methods allows you

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to take some of the different dimensions
of date and bring them to the fore front.

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So let's connect this back to some of
the things that we discussed previously.

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So, something like a tree map, right?

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A tree map takes, so, what are the most
visible elements in the tree map?

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Area.

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In the tree map the magnitude of the leaf

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is proportional to the area that
it contains, that it encloses.

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And if you think back to our few chapters
ago where we described what are the most

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salient features to human perception when
it comes to identifying differences?

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It's area, right?

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It was shape, excuse me,
it was location and area.

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So, by choosing to represent
magnitude in area,

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the tree map is making that
magnitude the most salient feature.

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Whereas, if you look at how
magnitude is represented in

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the chord diagram, it's actually
a secondary feature to layout.

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And what you can see is each of the nodes
on the edge the size of the node and

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it's relative location
to nodes next to it,

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demonstrate the,
those are the more salient features.

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So the things that stand out in this graph
the most are the edges around the outside,

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and the relationships that
are drawn between them.

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The Sankey diagram does the same thing for
relationship and it's encoding time and

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it's giving time,
in this particular example, to the x-axis.

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So when we look at this and
we say why is time so

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salient, it's because they've
taken position, the x-axis, and

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turned it into one of the most
meaningful features of the graph itself.

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So if you're thinking about how do
I choose which of the following,

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types of representation I,
to, to use for my own data.

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You can think about what
are the particular dimensions that have

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the most importance, and

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then which of these different encodings,
bring out those dimensions.

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And that's one of the ways that
you will end up looking for

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the ways that the most important parts of
your data become the most perceptible.