Graph Comparison Modes: Intersection, Difference, Combination, and Embedding

InfraNodus can be used to compare different discourses in order to identify how similar or different they are. This is particularly useful for comparing a company to an industry, a text you're writing to Google search results, and many other cases where you need to find gaps and relations.

Using this approach, you can reveal:

• The intersection between them 
• The difference between them
• Their combination
• How one embeds into another

Let us explain how this works and how it can be useful with a few simple examples. You can try it yourself using the graph comparison feature as you're reading this article. 

Suppose you have two graphs: one is a graph that lists different fruit combinations, and the other is a graph that lists different smoothie combinations. While we use the example of two graphs, you can do this operation for multiple graphs. But keep it mind that you always have the main graph (currently viewed) and the secondary one (what you're comparing it to).

The content of the first, Fruits, graph (let's call it the graph A — a secondary graph) are the two statements:

apples, oranges, bananas, and pears
kiwis and pineapples and apples

And this is how it looks visualized as a graph (the words are the nodes, and the co-occurrences are the relations, the topical clusters are indicated with specific colors, concepts that connect more topical clusters are bigger):

The content of the second, Smoothies, graph (the graph B — the current graph) are the three statements:

apples with kiwis
spinach with mangos and spirulina
apples and oranges

Let's see how the different graph comparison modes can be used to gain insight into the differences / similarities.

1. The Intersection Comparison Mode (the Overlap)

This mode shows the overlap between the two graphs. It takes all the relations in the current graph you're looking at (for instance, the graph B) and looks which of those relations ARE ALSO PRESENT in the graph A. 

It's similar to the AND logical comparison operation. Note, that it doesn't only take the nodes into account, but also the relations. This is why InfraNodus is much more useful than a standard text comparison tools because it shows you similarities and differences on a relational basis.

In our case, both graphs A and B talk about "apples" and "kiwis" in the context of the same statement (with a 4-gram sliding analysis window) and also the "apples" and "oranges". So the graph shows that the relation kiwi - apple - orange is present in both graphs. This is the overlap between them. 

A practical use case for it is to look at a discourse of a company and see how well it overlaps with a general discourse in this technology sector. The more intersections there are, the better the company serves the niche. 

2. The Combination Comparison Mode (Merge)

In this mode, we combine or merge the two graphs to see what are the relations that are present EITHER in the one, or in the other. It's similar to the OR logical operator and works for relations found in the both graphs:

As you can see, when we merge the two graphs, we also combine their clusters. It helps us see the structure of the discourse both texts produce.

This can be useful if you'd like to see what would be a synergetic effect combining two different companies, technologies, patent applications, or research papers together. 

For instance, in our case, combining fruits and smoothies together leads to the emergence of a big interconnected cluster that contains all the fruits.

3. Difference Between the Graphs

The difference mode is showing what are the RELATIONS present in the secondary graph (graph A in our case) that are NOT PRESENT in the primary current graph (graph B) — similar to the XOR logical operation.

In our case, that would be, what are the relations in the "fruits" graph that are not in the "smoothies" graph:

As you can see, the combination between "kiwis" and "pineapples" is only present in the text about "fruits", but we're not talking about it in "smoothies".  We did talk about kiwis in the both graphs, so if we simply used the concepts to show the differences, we wouldn't even see "kiwis" in thie graph. However, as we're focused on the relations, we actually see that the secondary discourse is bringing in a relation between "kiwis" and "pineapple", which was not in our primary one. 

We can also reverse this comparison and look the other way round: what are the relations present in the discourse on smoothies that are not present in the discourse on fruits:

Here we can see that the discourse on smoothes includes a relation between "spinach", "mangoes" and "spirulina", which is not present in the discourse on fruits. 

This approach can be very useful for analyzing what a company's discourse is missing in relation to another company or to the technology sector it's in. Or what a research paper is missing in relation to the other research papers on the topic. 

4. The Embed Mode (Discourse Infiltration)

The embed mode shows how well one discourse "embeds" into another. This can be used to estimate how well a new discourse fits into the old one, or how much a certain narrative infiltrated a certain context. 

In our case, if we take the current graph (B) — smoothies, and then click "Embeds" and choose the graph (A) — fruits, we would have a resulting graph that looks like the merge between the two, but where we highlight the graph B in relation to the graph A (red color): 

This graph shows us that the graph on smoothes did not mention a relation between "pears" and "bananas" (which existed in the graph on fruits), and it also doesn't mention "pineapples" (which were present in the "smoothies" one:

As you can see, the "fruits" graph is covering all the relations that exist in the "smoothies" graph. But it completely misses the relation between the "spinach", "spirulina", and "mango". So now we know that cluster that was unaffected by this infiltration!