Observations Regarding Graphlet Memorization

Carlos Martinez Quintero (Qualia Research Institute)https://www.qri.org/
Jul, 21 2023


This Summer Cohort’s QRI Visiting Scholars were tasked with memorizing thirty graphlets and recording their experience over the course of a week. We note that to do so, there usually was a preprocessing step to make the graphlets more easily memorizable, leveraging different types of memory. In particular, the following mnemonic techniques were the most effective:

  1. Narratives. Making stories that involved the graphlets was surprisingly effective.
  2. Embedding in 3D Space. Embedding particular graphlets in 3D space also aided memorization, possibly by decluttering 2D space.
  3. Clustering. Memorization was very rarely done in isolation – relating some graphlets to others and making groups really helped when memorizing a significant portion of the graphlets.

It was also found that other properties intrinsic to the graphlets, such as their symmetries and their planarity, made memorization easier.


A graphlet, as the name suggests, is a small connected graph. They can certainly be useful for graph-theoretic work, but there are other reasons we may care for them. There are a total of 30 distinct graphlets (with the number of vertices between 2 and 5) up to isomorphism. These objects are simple enough that one can ask a person to memorize all 30 of them in a few days, but complex enough that their memorization will not be a trivial task, and many things can be learned from such an activity. As a refresher on these topics, we suggest Jure Leskovec’s CS224W course, and in particular this lecture which covers graphlets.

Thus, as a phenomenology exercise to kickstart the 2023 QRI Summer Cohort, the three QRI Visiting Scholars (Riccardo, Ethan and Carlos) were tasked with the memorization of the first thirty graphlets (as shown in the picture above) over the course of the first week. They had to record their experiences, as well as any phenomenological observations. In this article we present a few important observations and insights we gather from these experiences.

The Search for Easily Memorizable Representations

The set of thirty graphlets, when seen for the first time (and before any patterns are found), seem somewhat arbitrary. It is therefore noteworthy that the three Visiting Scholars, who successfully memorized the graphlets (they were tested and everyone got all the answers correct), required that the objects to be memorized were first ‘processed’ into representations that could be easily memorized by them – the graphlets are divorced enough from our experience as to make it extremely difficult to just memorize them as they are. This ‘preprocessing’ was present in all three attempts, but interestingly, it was not always deliberate, as we will see. Furthermore, different people undertook the preprocessing in different ways:

Relational and Sequential Memorization

Something common to all three memorization attempts is that they always involved taking into account, in some way or another, the relations between graphlets: the number of graphlets which were learned ‘in isolation’, without relating them to others, was low. Carlos reported first trying to learn the graphlets through spaced repetition with Anki decks, but he found it to be difficult and time-consuming (although it must be noted that it is still possible to do so) – such an approach would possibly qualify as ‘memorizing the graphlets in isolation’.

Properties That Aid Memorization

There are representations that make use of the fact that we’re good at particular types of memory – such as narrative, or spatial. However, there are other properties that the graphlets as presented have which might also aid with memorization. Some possible properties are the following:

Other Approaches to Graphlet Memorization

The representations used were predominantly conceptual – however, this doesn’t have to always be the case, as there are many other sorts of representations that so far have been left unexplored: the state-space of consciousness is very rich. Riccardo suggests a dance choreography or sequence of bodily moves as possibilities, which would leverage muscle memory. He also suggested another direction that might be fruitful: embodying the graphlets, and using them as objects of meditation.


Graphlets are a particularly simple mathematical structure: but by virtue of them being mathematical structures, the experience of memorizing them may certainly give us insights into the memorization of, for instance, the 17 two-dimensional wallpaper groups (as mentioned in the Algorithmic Reduction of Psychedelic States), or four-dimensional regular polytopes. And of course, memorization of objects such as these can allow us to properly mathematically describe exotic states of consciousness, such as those experienced during meditation or psychedelic experiences.

Furthermore, the kinds of memorization techniques that seem to work best, as well as their phenomenological qualities, can give us insight into how the mind works and the nature of internal representations:

In other words, the sorts of mnemonic techniques that are the most effective can tell us a great deal about how internal representations are created in the mind.


I want to thank the other two QRI Visiting Scholars, Riccardo Volpato and Ethan Kuntz, for their detailed descriptions of their experience memorizing graphlets, for their insightful feedback, and for our fascinating conversations clarifying some of the ideas found in this article. Furthermore, I want to thank Andrés Gómez Emilsson and Hunter Meyer for their invaluable feedback and comments on the structure and content of this article.


Riccardo (stories):

4 nodes

5 nodes, part 1

5 nodes, part 2

Carlos (notable emergent graphlet representations):

Ethan (notable groupings and couplings)


graph theory, graphlets, mnemonics, phenomenology, math



For attribution, please cite this work as

Quintero (2023, July 21). Observations Regarding Graphlet Memorization. Retrieved from https://www.qri.org/blog/graphlet-memorization

BibTeX citation

  author = {Quintero, Carlos Martinez},
  title = {Observations Regarding Graphlet Memorization},
  url = {https://www.qri.org/blog/graphlet-memorization},
  year = {2023}