mind-viral immunity:   ?
stucture:   ?

The higher is the network's structure diversity and the higher is the alpha in the influence propagation score, the higher is its mind-viral immunity — that is, such network will be more resilient and adaptive than a less diverse one.

In case of a discourse network, high mind-viral immunity means that the text proposes multiple points of view and propagates its influence using both highly influential concepts and smaller, secondary topics.

The higher is the diversity, the more distinct communities (topics) there are in this network, the more likely it will be pluralist.

The network structure indicates the level of its diversity. It is based on the modularity measure (>0.4 for medium, >0.65 for high modularity, measured with Louvain (Blondel et al 2008) community detection algorithm) in combination with the measure of influence distribution (the entropy of the top nodes' distribution among the top clusters), as well as the the percentage of nodes in the top community.

The chart above shows how influence propagates through the network. X-axis: lemma to lemma step (narrative chronology). Y-axis: change of influence.

The more even and rhythmical this propagation is, the stronger is the central idea or agenda (see alpha exponent below ~ 0.5 or less).

The more variability can be seen in the propagation profile, the less is the reliance on the main concepts (agenda), the stronger is the role of secondary topical clusters in the narrative.

propagation dynamics: | alpha exponent: (based on Detrended Fluctuation Analysis of influence) ?   show the chart

We plot the narrative as a time series of influence (using the words' betweenness score). We then apply detrended fluctuation analysis to identify fractality of this time series, plotting the log2 scales (x) to the log2 of accumulated fluctuations (y). If the resulting loglog relation can be approximated on a linear polyfit, there may be a power-law relation in how the influence propagates in this narrative over time (e.g. most of the time non-influential words, occasionally words with a high influence).

Using the alpha exponent of the fit (which is closely related to Hurst exponent)), we can better understand the nature of this relation: uniform (pulsating | alpha <= 0.65), variable (stationary, has long-term correlations | 0.65 < alpha <= 0.85), fractal (adaptive | 0.85 < alpha < 1.15), and complex (non-stationary | alpha >= 1.15).

For maximal diversity, adaptivity, and plurality, the narrative should be close to "fractal" (near-critical state). For fiction, essays, and some forms of poetry — "uniform". Informative texts will often have "variable + stationary" score. The "complex" state is an indicator that the text is always shifting its state.

Using this information, you can identify whether the network has scale-free / small-world (long-tail power law distribution) or random (normal, bell-shaped distribution) network properties.

This may be important for understanding the level of resilience and the dynamics of propagation in this network. E.g. scale-free networks with long degree tails are more resilient against random attacks and will propagate information across the whole structure better.

If a power-law is identified, the nodes have preferential attachment (e.g. 20% of nodes tend to get 80% of connections), and the network may be scale-free, which may indicate that it's more resilient and adaptive. Absence of power law may indicate a more equalized distribution of influence.

Kolmogorov-Smirnov test compares the distribution above to the "ideal" power-law ones (^1, ^1.5, ^2) and looks for the best fit. If the value d is below the critical value cr it is a sign that the both distributions are similar.