Networks are Everywhere


When you hear "network" these days, chances are you think "social network" and then "social networking" and then Facebook.

In mid 20101 Facebook signed up it's 500 millionth member. That works out to something like one of every fifteen people in the world.

This picture (it looks like a map but it's really a network diagram — more on that in a moment) was created by a Facebook intern in 20102. It shows the world-wide pattern of Facebook "friends."

It's impressive to look at, but closer examination of what it actually shows, brings home some important, if subtle points relevant to this course.

  • THIS IS NOT A MAP. There are no country or continent outlines here. There are not dots for cities. All we are looking at is lines that connect the home cities of people who are Facebook friends. In other words, if I live in Oakland and I have a friend who lives in Chicago, our FB friendship contributes an arc between Oakland and Chicago to this picture.
  • All of the "morphology" (shape) and "topology" (what is connected to what) that is visualized here is the product of actual empirical relationship/interaction.
  • In other words, the "things" emerge from the "relations." That's going to turn out to be a sort of fundamental axiom of the NETWORK PERSPECTIVE.

How do they make these pictures

In case you are wondering how visualizations like this come about, here's a quick summary of the steps Paul Butler took.

It starts with raw data; in this case, a sample of about 10 million FB friendships in the form

vertex vertex
Dan Cornelia

The then uses the Facebook "application program interface" (API) to look up each user's home city. This information gets added to the data so now we have

vertex1 vertex2
Dan Cornelia
OaklandCAUSA BerlinGermany

Then we look up the latitude (north south) and longitude (east/west) of each city

vertex1 vertex2
Dan Cornelia
OaklandCAUSA BerlinGermany
37.73,-122.22 52.5166667,13.4

Then we plot the city points and draw lines between them and then we erase the points. But it turns out that this produces a blob.

Next we count up the number of times each pair of cities is mentioned and we note the actual distance between them.

vertex1 vertex2 latlong1 latlong2 numberOfFriends distance
OaklandCAUSA BerlinGermany 37.73,-122.22 52.5166667,13.4 3,013 5667 miles

Then the software draws the lines with different colors and weights and in different order depending on distance and number of friend pairs.

And finally, straight lines are replaced with great circles.

The point of running through that litany is to get you to make a mental note of the fact that great visualizations are a process. There's generally not just a piece of software that you can master and then just click a button to produce an assume visualization. Developing the capacity for formulating and executing such a process is one of the things you should take away from this course.

Not Friends, but Relatives…

The Facebook "world network" might be a symbol of the future, but networks of relationships are hardly new. Take, for example, the familiar idea of a "family tree."

This six generations of the Prince Ludwig I of Württemberg (ruled 1568–1593) are shown in this painting. The tree metaphor is often taken quite literally in these old family heirlooms. The underlying abstract tree structure that we see here, shows up in the kinship diagrams we use in anthropology and in the family trees we construct for medicine and genetics.

A Note about Trees

The structure we see in these diagrams is a special kind of network called a tree. A tree has the special properties of all the edges being directed and of not having any loops — that is, "travel" on the network involves no backtracking. We can speak of vertices being parents and children and of whole parts of the tree (subtrees) being the descendants of a particular vertex. We also have some intuitive relations and metrics — that is, ways of characterizing the network numerically: cousins and siblings, the aforementioned parents and children and generations in the "vertical" direction and "distance" in the horizontal that lets us talk about first cousins and second and so on. And note the relation between these two: what kind of cousins we are depends on how many generations you have to go back to find a common ancestor. This kind of thinking shows up in the overlap between networks and graphs and biology in the field of cladistics and genetics where we want to talk about how "far apart" individuals or species are.

Biological Networks

And speaking of biological networks, another biological relation that generates networks is "who eats whom?"

We are familiar with the phrase "food chain" from everyday discourse. Although often caricatured as the little fish getting eaten by the slightly bigger fish getting eaten by the slightly bigger fish getting eaten by the slightly bigger fish getting eaten by the big fish, there are typically different species at each level (that is to say, it's a tree, not a chain). A slight extension of this idea recognizes that who eats whom is not always a nice, neat hierarchy (that is there are loops) AND that eventually, even the big things die and then they are scavenged and broken down by little things. We call this a food web.

After we take a look at a few, let's try one ourselves.


File nameFile typeSize
Ryan-NetworksAreEverywhere(1).pptxZip archive data17.04 MBInfo
Ryan-NetworksAreEverywhere.pptxZip archive data6.94 MBInfo


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Cook, Jim. 2009. Cosponsorship Networks in the U.S. Senate as of March 1, 2009

[ UCLA Mathematicians Solve Violent Los Angeles Gang Crime with Math

Butler, Paul . 2010. Visualizing Facebook Friends: Eye Candy in R