A standard for presenting network visualizations

I just attended an exam on controversy mapping at Aalborg University, where among other things students interpreted Gephi visualizations of different kinds (pic related). There were networks of Wikipedia pages on Parenting. The students were quite good despite common issues about how to talk about networks. The exercise is hard, and we do not expect most students to master it in the time of the course (in this case 3 weeks full time). It is nevertheless true that in my view, there is a standard way to present your network visualization. I realized that it would be useful to share my educated opinion on how you should present your network.

Let me first address two possible misunderstandings.

  1. It is not about your method. There are infinite amounts of valid research designs that involve network visualization. I am not the fun police. I will not discuss which are good or bad.
  2. It is not about evaluating the layout quality. That is a very valid topic, I have a lot to say about it, and it is something crucial that comes to mind when reading something like “the gold standard for network visualization”. However it is not what I mean here.

What I want to address in this post is which aspects you should cover, in which order, and more importantly how you should cover them. If you ever felt lost in an argumentative maze while presenting your network, stay with me.

But before I start suggesting what you should say and how, I need to introduce what I consider the four key layers of any discourse on a network visualization. I will take the time to detail them, for the moment I will just mention their existence with the picture below. If you are familiar with Bruno Latour’s work, you may recognize a chain of reference. If not, you will understand along the way: the key thing is to acknowledge the translations between the layers.

Layers to convoke when presenting a network visualization

What you should say

We assume the classic situation: you are presenting network maps made by yourself. You know all there is to know about the process, from harvesting to refining and to visualizing. You have some expertise on the topic. Your audience starts with a very open question such as “Can you tell us what this is about?”.

1. State the purpose of the work

State the topic first, your research questions if you have some, and/or what you tried to achieve.

It can be very short but it is still important.

We never visualize a network for the sake of visualizing a network. There is always an underlying motive. Interpreting a network is never simple and you and your audience are at risk to get lost in the process. Stating where you are headed to helps.

2. Describe what the visualization translates

Explain concisely the process that has lead to the visualization. It is a chain with many steps which requires clarity. Use the proper terms and make visible how each step leads to the next explicit.

There are two valid strategies to narrate this, depending on the situation:

  1. Describe the process in a pseudo chronological order, from harvesting to visualization.
  2. Start with the physical object (the printed sheet, the screen…) and go upstream towards its origin.

Pick whatever makes you comfortable. You might want to leverage this occasion to explain the process, or you have done it before and you want to be straight to the point. In both cases there are a number of elements that you must provide.

You must explain the key steps of the process and use the proper terms to talk about each of them. Here I will use strategy number 2, ie. to narrate the steps starting from the physical object and going upstream through the process. There would be variations depending on your research design, I will just assume the common situation described in most Gephi tutorials.

In a nutshell, each step of the process is one of the four layers I introduced previously. Each layer is translating the layer just below, and the goal is to make each translation explicit.

Describe how the image translates the network

The image or map is the physical object that you empirically offer to your audience to understand your work (along with your explanations of course). You must explain where every thing visible in the image comes from. In a typical scenario this would be for example:

  • The image has been produced by visualizing a network.
  • The rounds are representing the nodes. All nodes have been represented.
  • The lines are representing the edges. All edges have also been represented.
  • The texts are nodes’ labels, we only displayed the most important ones.
  • The size of each round represents the degree of the node.
  • The color of each round represents the category of the node.
  • The thickness of a line represents the weight of the edge.
  • The color of lines has been set to a light grey to avoid too much visual cluttering.
  • The placement of the nodes has been decided by an algorithm analyzing their connections, not considering other attributes like their category.
  • The legend precises the color coding of node categories and the scale of edge thickness.

Explain how The layout works

The layout algorithm must be explained. In the case of Force Atlas 2 and many others, the important points are:

  • The layout places the nodes only in function of their links, it ignores all attributes.
  • It works iteratively by having all nodes repulse each other and connected nodes attract each other. By design it converges to an equilibrium that depends on the random starting positions.
  • The resulting projection is said isotropic: it has no specific axes and could be turned or flipped without losing its features. Is is supposed to be interpreted in terms of relative distances.

In case such settings are used, those also deserve to be mentioned:

  • Gravity: an additional force limits the spreading of the nodes, which brings a minor bias but allows to optimize space during visualization.
  • Prevent overlap: the placement of nodes has been adjusted so that they do not overlap, bringing a minor bias but optimizing readability during visualization.

Note: I do not think it is worth formalizing an additional layer, here a mathematical projection to a 2D space, even though it is what we actually do.

Describe how The network translates source data

The network or graph is the list of nodes and the list of edges used as a data structure in a software like Gephi. The network is translated visually by the image, but it is not the image. Similarly, it often translates less refined data, but is not that data.

You must explain what the nodes and the edges represent. In other terms, you must describe how they relate to the raw data (see below). For instance:

  • Nodes represent words mentioned at least 10 times, excluding a list of stop-words.
  • Edges represent co-occurrence, that is when two words appear in the same document.
  • The weight of edges represents in how many documents the words appear together.

Explain how source data refer to the empirical world

You must explain where source data come from and how they were picked. The choice of data to study often stems from an interest in something precise in the empirical world. It might be parenthood, #blacklivesmatter, Nordic design… Whatever is your topic or research questions, it provided an interpretive framing of the source data, for instance because certain elements are used as proxies to obtain information on your original object of interest.

It might be for instance to mention that you were interested in a topic involving gender issues, but for practical reasons it had to be specific enough, which lead you to pick the Parenting topic already delineated in Wikipedia.

3. Interpret your network map

Now that your audience knows what all of this is about, you can discuss the content of your network map. Your interpretation will consist of a number of statements that will rely first on the image and traverse layers down to the empirical world if possible.

There are many ways to organize your interpretation. You can refer to the suggestions Tommaso Venturini, Debora Pereira and I have proposed for visual network analysis. I will not open that discussion here. The only important thing is the gist of any argument of that kind: it exposes features of the network that are visible in the image, and argues that these features originate in the source data in a way that allows to say something on the empirical world. This interpretative path is long, I know. Sadly, such is the situation you are facing. Science is hard.

You must always be clear about the translations when you make your points. This is the one and only trick. Succeed at this, and you will master network interpretation. Making a good point is all about finding your way through the layers. It is hard though. I will dedicate the rest of this post to breaking down that question.

How you should say it

Pay attention to the vocabulary

The bread and butter of your arguments is the logical connections between the many elements you will convoke. There is so much to say that I will not even try. However it always starts with using the proper vocabulary. This question is critical here because as we will see, using the proper terms is your best defense against treacherous argumentative lines that will lead you into a maze of fallacies.

Each layer has its specific vocabulary, let us start by reviewing this.

image / map

The following vocabulary is apt at describing the image:

  • Circle, shape, line, text
  • Colors, light, dark
  • Big, small
  • Close, far
  • Busy/dense/full/occupied areas, holes, blank spaces
  • Center, periphery (of the image, of a zone…)

DO NOT USE to describe the image itself: node, edge, hyperlink, web page…

network / graph

The following vocabulary is apt at describing the network:

  • Node, vertice
  • Edge, link , connection
  • Node/edge weight, attribute, modality of an attribute
  • Degree, indegree, outdegree, centrality metrics
  • Density (of a set of nodes)
  • Neighbors, leaves (nodes with 1 neighbor), orphans (0 neighbor)
  • Structural equivalence (having the same neighbors)
  • Geodesic distance (length of the shortest path)
  • Clusters (as the outcome of a clustering algorithm)
  • Modularity (of a clustering)

DO NOT USE to describe the network: being close or far, being grouped…

You will often want to do simple countings, like saying that a set of nodes is big, or small, or bigger than… A set of nodes can be a cluster, nodes where attribute X takes modality Y, nodes of a degree of X or more, neighbors of X…

Source data

This step is not always only one step in the process, and can take many shapes. The important point is that data have always been transformed: they have been cleaned, filtered, refined… There are so many possibilities that I cannot provide an overview. I will just cherry pick a few examples.

If your raw data is Wikipedia pages, the following vocabulary applies:

  • Web page
  • Hyperlink, hypertext link
  • In text links, “see also” links

If your raw data was a set of documents in a co-occurrence analysis:

  • Text, document
  • Paragraph, expression, n-gram, word
  • Co-occurrence
  • Term frequency

Your data might be from a patents database, from Twitter or Facebook, from a qualitative sourcing… Each of these cases have their own types of objects, relations and vocabulary.

DO NOT USE to describe the raw data: node, edge, being connected, being close, being grouped…

Empirical world

The vocabulary you use when you refer to the empirical world can be:

  • People, institutions, actors, …
  • Books, projects, ideas, …
  • Topics, academic fields, interests, …
  • Friendship, accointances, affinities, …
  • Groups of peoples, community, culture, …
  • Notoriety, influence, authority, relevance, …

Beware of metonymies

In practice you want to say “the size of the nodes” and not “the size of the rounds”. Fine, but you are playing with fire. If you master the exercise you are able to use all sorts of shortcuts because you know the limits. A naïve listener might be under the impression that most of the concepts are interchangeable and that you can indifferently say line, edge, link or hyperlink. It is very wrong. The issues are real and you might trick yourself into fallacious arguments and circular logic.

Be clear about what is representing and what is represented

The line not to cross is made clear by looking at how we understand a metonymy, a figure of speech where we refer to something by using a different but closely related concept. For instance “swearing loyalty to the crown” refers to the sovereign and not to the physical object, of course. We are able to get the right meaning because it would make no sense to swear loyalty to a literal crown. The context tells if the word is metaphorical or literal, if there is a metonymy or not. The same applies to our concepts. Insofar as nodes do not have a size (they are abstract network entities) it is clear the “node sizes” refers to “the size of the shapes representing nodes”. In that sense the shortcut is valid, but remains tricky because we use the word node to actually refer to shapes, and this dangerous shift is how accidents happen. The line not to cross is when metonymies become ambiguous.

How you trap yourself into the maze of circular logic

First you say “those nodes are close”, which can only be understood as a metonymy for “those shapes representing nodes are close”, then you say “so they form a cluster” and you are already stepping on the forbidden limit. As a teacher I will often ask to clarify the ambiguity, for instance: “Can you precise why they form a cluster?” Because you know the process, you understand that node placement results from the layout algorithm, which is
indeed what I expect. However at this point the confusion can make you happily walk into to the maze of circular logic, by answering something like: “It is a cluster because the layout algorithm placed the nodes close to each other”. You might well explain how the algorithm work, but it does not matter, it is too late. You have trapped yourself into a fallacy – can you see why?

The argument is circular because it states that close nodes make clusters and clusters make close nodes. Unfortunately, being aware of the circularity does not really help. From my experience I know that you only realize that you are lost when it is far too late – if you ever do. Avoiding the fallacy is not about recognizing the forbidden zone, it is about not stepping into the maze. It is about having a practice that never puts you at risk.

What is the safe practice? First of all, it is to use the proper vocabulary. But I cannot win the fight against human nature and make you stop using shortcuts. So the safe practice is about using protections. Always check the layer where your argument is valid. The entry to the maze of circular logic is where confusing metonymies give birth to arguments with layers mismatch. But layers mismatch can also lead to less dramatic forms of bad arguments that can be very detrimental to you despite their low profile. We will see how checking layers helps to debunk those.

Bad arguments

There are different degrees of bad arguments, corresponding to the different ways you can fail to circulate the chain of reference from one layer to the next.

Tautology: stuck in a layer

The worst type of argument is when there is no argument. A simple description posing as a point. The lipstick of rhetoric on the pig of triviality. For instance: “The pro-life cluster separates from the pro-choice cluster by sustaining a sensible distance”. The argument is circular: the clusters are distant because they are distant. I diagnose this bad argument as a complete failure to circulate out of the top two layers, the image and the network.

You can debunk such statement by checking the layers. Making a point involves multiple steps where features of one layer are related to the next. A proper argument would look something like this:

  • The pro-life and pro-choice nodes appear distant in the image.
  • They are distant because they have only few connections. That is how the layout algorithm works, but we can also see that there are less edges between clusters than inside each one.
  • The bigger amount of edges inside clusters shows that actors tend to connect to those who are similar to them, and ignore those who are different.
  • This behavior (homophily) reveals an opposition between the two communities.

Naturalisation: jumping to conclusions

A bad but less bad type of argument is to jump over translations, making an incomplete point. I call this “naturalization” because jumping to conclusions often uses the rhetoric of evidence, as if the visualization was a natural manifestation of the empirical world. For instance: “the pro-choice are grouped together, showing they share common values”. The conclusion is sometimes true, but the argumentation is poor. As a teacher I would immediately ask: “can you explain why you think a group of nodes implies the sharing of common values?”, giving you a chance to show your ability to circulate between the layers – or making you realize that you are lost in the maze of argumentation. Some students just use shortcuts, and when asked to unpack their reasoning, they can do so.

Once again the safe practice is to check the layers involved. In this example, proximity belongs to the image layer (number 1). Sharing common values belongs to the empirical world (number 4). You must progress from layer to layer without jumping over any. Respecting the vocabulary helps to not confuse the layers:

  • The proximity of the pro-choice in the visualization…
  • …comes from the important amount of edges between the nodes…
  • …which reveals that these actors know and link each other on the web.
  • We hypothesize that it might be because they share common values.

In this example the last point is not very convincing, and probably just false. The form is valid but not the content. That was just an example but it remains true that the last translation, from the source data to the empirical world, is the most difficult. Unfortunately, it is also the most important.

Run the last mile

My last piece of advice is to always run the last mile: your arguments must lead to conclusions on the empirical world, even if only in a hypothetical way. The finish line is the real world. The reason why you analyze data is because you want to understand something about the world, and you must demonstrate your ability to do so.

Not running the last mile is the most tragic pitfall because it happens only to good students, those who went far but could not defeat the last boss. Bad argumentation does not lead you to the last mile, but you can have all your arguments valid and still not reach the finish line.

Not running the last mile produces analytically valid statements but only about the data. For instance, not mentioning the argumentation but just the conclusion:

  • …hence the governmental websites occupy the central positions in the NGOs corpus.
  • …all NGOs are citing each other on the web, except humanitarian associations.
  • …the websites of the radical left are well connected within the left-wing web sphere but do not form a cluster, being poorly connected to each other.

Those claims may be technically valid, they do not explain well how it relates to the empirical world. The kind of argument that I expect goes a little further, even if only in the form of hypotheses, for instance:

  • …possibly because many NGOs depend on governmental funding, which often require to link to the funding institutions.
  • …because humanitarian associations are in competition for donations, which may lead them to not cite their competitors.
  • …despite being gathered under the common label of “radical left”, these actors do not acknowledge each other and do not form a community, possibly because of ideological divergences.

While you are here…

If you are interested in the works of the Aalborg University students, you can look at their work down below:

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