Challenges of optimizing representation of polyhedral clusters of preoccupations

Interactive Polyhedral Configuration of Preoccupations (Part #3)

As noted above, four factors determine the manner in which a polyhedron approximating to a sphere is represented in a force-directed display. These are termed, force, charge, gravity and link distance. If these are not optimized for a polyhedron of a given complexity, the configuration may disappear off the screen, be too large, or be too small. This is a known technical issue discussed separately (Optimize d3 force directed layout, via charge/gravity properties, based on number of nodes, StackOverflow). One simple means of circumventing this to some extent is to change the magnification of the screen -- offering other advantages and disadvantages, partially dependent on the dimensions given to the window within which the display is presented.

There is the further concern that force-directed applications may be differently supported on different platforms and browsers -- especially when they are subject to periodic updates. Applications which worked well at one time may no longer operate if no provision is made for backwards compatibility.

In the case of social networks of any kind, force-directed displays have further enabled the well-developed efforts to visualize such networks, as clarified by Tommaso Venturini, et al (What do we see when we look at networks: Visual network analysis, relational ambiguity, and force-directed layouts, Big Data and Society, 8, 2021, 1).

These algorithms may be implemented according to different recipes but they all rest on the same physical analogy: nodes are charged with a repulsive force driving them apart, while edges introduce an attractive force between the nodes that they connect. Once launched, force-vectors vary the position of nodes trying to balance the repulsion of nodes and the attractions of edges. At equilibrium, force-directed layouts produce a visually meaningful disposition of nodes, where nodes that are more directly or indirectly related tend to be closer.

This technique to visualize graphs has become so common that we often fail to notice its accomplishment. Force-directed layouts do not just project networks in space—they create a space that would not exist without them. This is why this process is better called “spatialization” rather than "visualization". Spatialization creates a space in which the multidimensionality of networks can be flattened, in a process of "graph embedding"... that has applications even outside visualization. Spatialization creates a space that retains key properties of a network. [emphasis added]

In considering how to optimize the configurations, of particular interest is the "metaphorical" interpretation of force, charge, gravity and link distance from the perspective of the psychosocial and communication sciences in which those terms are frequently used -- but with other connotations. For example link distance has been associated with conceptual distance by Anthony Dekker, offering many illustrations and animations (Conceptual Distance in Social Network Analysis, Journal of Social Structure, 6, 2005). That journal offers many other papers of relevance.

An interesting feature of the experimental exercise were the constraints of the experimenter in exploiting the many possibilities of force-directed layout. As a metaphor in its own right, whilst access to relevant expertise is possible in principle, acquiring timely expertise typically proves to be a considerable constraint in practice -- despite the helpful response in many fora (as illustrated by the StackOverflow case).

Given current debate regarding the problematic aspects of AI, there is therefore considerable irony to the instant availability of useful advice from ChatGPT, for example. This enabled many force-directed properties to be enhanced -- despite the relative ignorance of the experimenter in that regard.

Question to ChatGPT: Unfortunately the current selection of the force-directed parameters for linkdistance, gravity and charge do not separate the nodes of the polyhedron into an approximately spherical form in order to enable any inadequacies to be apparent. This issue of adequate separation is apparently a known issue. Do you have any comment on an optimum combination of values of those parameters

Response from AI : Determining the optimum combination of force-directed graph parameters, such as link distance, gravity, and charge, can be a complex task as it often depends on the specific characteristics of the graph and the desired layout outcome. Achieving an approximately spherical form for a polyhedron can be challenging, especially when dealing with complex and densely connected graphs.

However, you can try adjusting these parameters to see if you can achieve a better separation of nodes. Here are some general guidelines:

Link Distance: This defines the desired length of the links between nodes. Increase the link distance to encourage more spacing between connected nodes. Increasing this value will cause the links to stretch, resulting in a more sparse layout. This can help prevent nodes from overlapping and provide a clearer visualization. Experiment with different values to find a suitable balance.

In psychosocial networks, the metaphorical interpretation of distance can represent the perceived psychological or social separation between individuals or groups. It implies the level of similarity, familiarity, or emotional closeness within the network. The distance metaphor suggests that individuals who are psychologically closer are more likely to have stronger connections and interactions, while those who are psychologically distant may have weaker or limited connections.

Gravity: This parameter attracts all nodes towards a central point. Higher gravity values will pull the nodes closer to the center of the visualization. Increasing the gravity value can help in spreading out the nodes more evenly.

In psychosocial terms, the metaphorical concept of gravity can represent the natural tendency for individuals to be drawn to or influenced by others based on various factors such as attractiveness, authority, charisma, or common interests. It implies the pull that certain individuals or ideas have within the network, attracting others and influencing their behaviors or beliefs. The gravity metaphor suggests that some individuals have a stronger ability to attract and engage others, leading to the formation of clusters or subgroups within the network.

Force: This parameter controls the overall strength of the forces acting on the nodes. Higher values will result in a more energetic layout, while lower values will yield a more relaxed layout.

In psychosocial networks, the concept of force can metaphorically represent the influence or impact that individuals or groups exert on one another. It implies the strength of connections, the persuasive power, or the ability to drive change within the network. The force metaphor suggests that certain individuals or ideas have the potential to create a significant impact on others, shaping their behaviors, beliefs, and attitudes.

Charge: The charge parameter determines the repulsive force between nodes. Higher charge values will make the nodes repel each other more strongly, leading to a more spread-out graph.which can help in separating nodes further apart. However, excessively high charge values can lead to excessive node scattering. It's recommended to start with moderate charge values and adjust accordingly.

When used metaphorically in psychosocial networks, the concept of charge can represent the emotional or psychological energy associated with individuals or groups. It implies the positive or negative charge that individuals bring to their interactions and relationships within the network. A person with positive charge might be characterized as uplifting, inspiring, or motivating, while someone with negative charge might be perceived as draining, demotivating, or even toxic.

Additionally, you may consider other layout algorithms specifically designed for spherical layouts or polyhedral graphs, as they might provide better results for your specific use case. Keep in mind that achieving a perfect spherical form may not always be possible, especially for graphs with complex connectivity patterns. It's important to strike a balance between aesthetics and preserving the underlying graph structure.

The reference to spherical layouts engendered the following of potential relevance:

Oh-Hyun Kwon, et al: Spherical layout and rendering methods for immersive graph visualization (2015 IEEE Pacific Visualization Symposium (PacificVis), Hangzhou, 2015)
Dario Rodighiero: Drawing Network Visualizations on a Continuous, Spherical Surface (2020 24th International Conference Information Visualisation (IV)).

Whilst the parameters could be readily modified, the challenge remains how to determine the balance between them for a meaningful display. A potentially helpful indication in that regard is the interactive Spherical Force Directed Layout (Codepen, 2023) enabling parameters to be adjusted to render the results accordingly.

Question to ChatGPT: Could you clarify your helpful articulation of what is effectively a "3-body problem". I understand the need for experiment. Can you suggest useful values for each as a point of departure -- perhaps in the light of your suggestion for adaptation to spherical form.

Response from AI : While the force-directed graph layout is a simplified representation of the physical "3-body problem," it shares some similarities in terms of balancing attractive and repulsive forces between nodes. Here are some initial values you can use as a starting point for each parameter:

Link Distance: Start with a value that provides some initial spacing between connected nodes. Depending on the scale of your graph, a value between 20 and 100 might be a reasonable starting point. For example, you can begin with a link distance of 50 and adjust from there.
Gravity: Begin with a moderate gravity value to encourage nodes to move towards the center. A value between 0.1 and 0.5 can be a good starting point. You can start with a gravity value of 0.3 and adjust it as needed.
Charge: Set a moderate charge value to balance the repulsion between nodes. A value between -500 and -2000 might work well. You can start with a charge value of -1000 and experiment from there.

Keep in mind that these suggested values are not universal, and the optimal values can vary depending on the specific characteristics of your graph, such as size, density, and desired layout outcome. It's important to experiment with different values and observe the effects to find the configuration that best suits your needs.

Additionally, consider adjusting other parameters specific to the force-directed layout algorithm you are using, such as the cooling factor, iterations, and temperature, as these can also influence the layout outcome.

Remember to iterate and fine-tune the parameters based on the observed results, and don't hesitate to experiment with different combinations until you achieve a satisfactory visualization that aligns with the desired spherical form.

In response to such suggestions, the application generating the displays was adjusted to ensure that a different combination of parameters was used for polyhedral displays of different complexity. The possibility of identifying optimal combinations remains a continuing concern -- notably dependent on the number of nodes and the size of the screen display. [NB: Developers have noted that browsers tend to reload a previous display, even when modifications have been made. Clearing cache may not suffice. Changing the file name is guaranteed.]

Noteworthy is the experience of multiple iterations of the optimization process for a given layout which, as a metaphor, merits comparison with an elusive combination of rodeo riding, tuning an instrument, and ensuring appropriate tensional integrity (as in a tensegrity) -- potentially to recognized as the fndamental challenge of governance (Governance as "juggling" -- Juggling as "governance": dynamics of braiding incommensurable insights for sustainable governance, 2018).

Ideally, with further development and additional expertise, users could themselves be enabled to modify relevant parameters in order to adjust displays in quest of focus and significance, according to preferences. Users could themselves specify the keywords with which a display could be generated -- avoiding the production of multiple experimental displays. This may be a possibility which search engines and web browsers will offer (as noted above), now that these facilities are being extensively promoted as "AI-enhanced".

Of some relevance to any articulation in graph form as explored here, is the extensive literature on the "readability" of displays in relation to their "aesthetics", of which examples are noted in the references below. This usefully highlights the question of the "readability" of any listing of organs of governance and their preoccupations of which the UN's 17 Sustainable Development Goals offer a prime example, as discussed separately (Coherence of Sustainable Development Goals through Artificial Intelligence, 2023; Memorable Packing of Global Strategies in a Polyhedral Rosetta Stone, 2023).

As an intriguing technical parenthesis, the link pattern for the most complex Archimedean polyhedron had been incorrectly derived for this exercise from the OFF file exported (like the others) from Stella 4D. The resulting polyhedral display was a mess. The difficulty is that OFF files specify edges around a polyhedral face, not the vertex pairs required for the force-directed displays. The conversion, whilst logical, is tedious for complex polyhedra. ChatGPT proved willing to convert the OFF file to the required adjacency list. Unfortunately the result was erroneous -- willingly corrected through several iterations by ChatGPT. It remained erroneous. It then proved easier to produce a simple program which would convert any such OFF file into an adjacency list. This reinforces the concern that AI can generate errors about which it is necessary to be vigilant. On the other hand, without timely access to human expertise, ChatGPT proved especially helpful in indicating amendments to the d3.js coding by which the force-directed displays were rendered.