Narrative Influence Propagation Dynamics

InfraNodus has a network structure measure — alpha score — that can measure narrative influence propagation dynamics. This measure can be important for text classification, understanding the rhythmical structure of a narrative, and its objective: whether it is to reiterate, persuade, inform, or explore. 

The lower the alpha score (e.g. ~ 0.5) of a narrative, the more likely the most influential concepts will appear at regular intervals as we read through it. This means that the text is more rhythmical, has less dynamic variability, that it delivers the narrative in a steady, cyclical flow, reiterating certain concepts in regular intervals. Such narratives will often have an objective to persuade or to convert a reader to a certain idea, as they make use of rhythm as a rhetorical device. 

The higher the alpha score (e.g. ~ 0.6-0.7) of a narrative, the higher the variability of influential concepts appearing throughout the text as the narrative unfolds. This means that some parts of the narrative (e.g. at the beginning) might focus on the main concepts, but then (e.g. towards the end of the narrative) some other parts will become more specific and will not be related to the most influential concepts anymore (e.g. zooming in or going on a tangent to explain a certain specific issue). Such texts will more often be associated with explanatory or exploratory functions as they present the main ideas first and then start exploring the less influential ideas.

If we make an analogy with a social network, the first case (low alpha) is if throughout your life you tend to meet influential people on a regular basis, almost weekly, as if it were your job. The second case (higher alpha) is if throughout your life you sometimes hang out with influential people, but you also have periods when you withdraw and spend your time alone or with a small circle of friends or colleagues who are not so influential, but that maybe allows you to discover some deeper parts of yourself, which are more introvert in nature.

So how does it work?

Static Network Structure Measures

Consider a network where every node has a measure of global influence (in InfraNodus, it is based on betweenness centrality, which shows how important the node is to connecting network on the global level, between the different communities). Both social networks and text networks represent a certain process that happened in time. If we simply look at the structure of the network, the communities, the most influential nodes, we can see a snapshot of this process and general tendencies on the global level.

For example, a dispersed network with distinct communities that are disconnected, indicates that certain nodes interacted more often than others and that there is a strongly pronounced community structure present in this network. This information, however, will not inform us about the nature of the dynamics behind that process. It could be that as the process evolved, we jumped from one cluster to another. It could also be that we stayed in the same cluster for a prolonged period of time and then moved on to the next, and so on. 

This is where influence propagation measures can be useful to understand the nature of this dynamics.

Dynanic Network Structure Measures

In influence propagation, we don't just look at the snapshot of a network's topology but, rather, trying to get some insights about its evolution.

In InfraNodus, we assign a measure of influence to every node on the global level, based on betweenness centrality. 

We then traverse the text network, from the very first statement until the last, and record the influence score of every word (node) as it appears in a text. 

We then build a graph, available in the Analytics > Structure panel, which shows how the influence propagated over time, as we traversed the discourse network (see the two examples below to understand the difference).

The horizontal X-axis shows the sequential number of the node (word) in the total sequence. It takes into account the unique occurrences of the lemmatized nodes, minus the stopwords. 

The vertical Y-axis shows the difference of the influence (BC-based) in relation to the previous node, indicating how much the influence changes after each step. 

In the first graph above, we can see that there are rhythmical spikes of influence as the narrative unfolds and, thus, lower alpha (0.51). Towards the end they are smaller, but yet the distance between them is more or less the same. This means the narrative is rhythmical and that the most influential concepts tend to emerge at equal intervals throughout the text. As we use betweenness centrality as the measure of influence and those nodes tend to connect different topics together, we can also say that this text may also be regularly shifting between different topics bypassing the most influential concepts. Formally, it can be represented as something like "X is important and through B it links to Z which is also linking through A to Y, which, in turn, links through B to X again". Such texts are made to persuade or to inform as they employ rhetorical devices and reiterate the most influential concepts in a rhythmical fashion.

The second graph has a higher degree of variability in influence propagation. Higher alpha (~ 0.64) and much more variable and diverse graph. The spikes of influence occur, but not in a rhythmical pattern, which means that the most important concepts and the shifts between the topics occur irregularly. This indicates a narrative that has a tendency to change rhythm and to go into various topics deeper, sometimes staying in one of them for a longer period of time, even if it's talking about the concepts that are not the most influential ones in a discourse. Such texts will generally be more adaptive and have explanatory or even exploratory nature. They do not attempt to tell us how things are, but, rather provide an account of what might be, exploring peripheral ideas and letting the tangent thoughts unfold. Formally, it can be represented as something like "X is important and through B it connects to Y, which is also talking about S, T, U, and K, but coming back to Y we have to also say that through A it links to Z, which links through B to X, which, in itself is also talking about I, J, and K." As you can see, there is a higher level of diversity here than in the first example. The narrative propagates based more on the smaller, less influential concepts, zooming into specific topics and exploring the detail. 

How it Works: Detrended Fluctuation Analysis

In order to calculate the variability of influence as the narrative unfolds, we use the same rhythm that is used to calculate heart rate variability (HRV) as it is a proven method used in clinical applications.

We plot the narrative as a time series of influence (using the concepts' betweenness score). We then apply detrended fluctuation analysis to identify the 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 the 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 a "variable + stationary" score. The "complex" state is an indicator that the text is always shifting its state.