Betweenness Centrality

The same three settlements emerge from two independent bodies of data

The dissertation sets it out thus: “first, the points low in betweenness centrality are Kami-Kaiden, Tsuka and Tonyū. And their respective accent forms are kō type for Kami-Kaiden, intermediate type for Tsuka and otsu type for Tonyū. In the data on customary practice, the singular points are Kami-Kaiden, Tsuka and Tonyū, which coincide with the points low in betweenness centrality”.

The content of the departure is examined as well: “moreover, the scores of the correspondence analysis show that these singularities are not mutually similar in character but arise from disparate characteristics. From this it is clear that, as regards customary practice, the distinctiveness of each settlement is strong”. The reading, that is, is that the three settlements do not depart in the same direction but each in its own.

The interpretation built on that is: “that characteristics appear at the same settlements in entirely distinct phenomena suggests the possibility that each phenomenon is constrained by geographical conditions. One of those geographical conditions is what could be analysed on this occasion as betweenness centrality”. Betweenness centrality is offered as a candidate for the condition governing both accent and custom from outside.

This is a priest’s route, not the movement of ordinary people

The edges of the graph are the circuit route of priests from Jōshōji in the early modern period. They are the roads used by Shin Buddhist priests to make the round of the villages of their parishioners; they do not record the villagers’ daily comings and goings, the carriage of goods, or the traffic of marriage. The betweenness centrality obtained here is therefore, strictly, “the degree to which a point is likely to become a place of passage within the network of a priest’s circuit”.

Tying that to the transmission of language and custom requires the premise that “the roads the priests travelled were also the roads people and goods travelled”. That premise is not tested in the materials. The dissertation itself lists among its tasks that “it is also necessary to investigate the existence of settlements not included in the circuit route used here, and whether there was interaction with them”.

There is in fact a passage showing that the circuit network is insufficient for explaining the linguistic distribution within the village. On why Kadonyū shows the kō type, the dissertation invokes not the circuit route but marriage relations: “it is known that marriages were frequently contracted with Sakauchi Village, which lies beyond the road further to the west”. The influx of a linguistic system through marriage is a route that is not in this graph.

An early-modern route is being used to explain a linguistic distribution recorded in the twentieth century

The network is built from an early-modern circuit route. The accent data, meanwhile, are Sugito’s report contained in Nomura (1977) (surveys of 1971 and 1976), and the data on custom are from the national survey of customary practice of 1949–50. The periods of the materials are several centuries apart.

The dissertation states this itself: “in the present study, only the early modern period was made into a network, but the presence or absence of movement of people and goods along traffic routes changes with the passage of time. It is therefore necessary to divide the early modern, modern and contemporary periods, trace the transition, and explore the aspect of linguistic diffusion concretely in connection with extralinguistic factors”. It also says that “the traffic network with the regions to the north and east of Tokuyama Village has been clarified to a degree by the present circuit route, but the traffic networks to the west and south also need to be reconstructed”.

If one takes linguistic change to have proceeded under early-modern traffic conditions, the difference in period is not a problem — but that is an untested assumption. Which state of traffic, at which point in time, bore on which linguistic state at which point in time, cannot be judged from the materials.

Adding difference in elevation in the same units as horizontal distance has both a warrant and an arbitrariness

The equation in the 2012 presentation materials takes the square root of the sum of the squares of horizontal distance and difference in elevation as they stand. Geometrically that is straight-line distance along the slope, but as a cost of movement it underestimates the effect of elevation. In the dissertation, indeed, it is revised into the form multiplying the difference in elevation by 8.3, and values computed from the same data diverge: 658 against 682, 3541 against 3632.

The coefficient 8.3 has a warrant in Langmuir’s rule of thumb. But that is one way of fixing a coefficient, not the single right answer — as the dissertation itself writes, “as for walking cost, the problem also arises of which of the many model equations one ought to select”. Choose a different walking-cost model and the edge weights change, the shortest paths change, and the betweenness centrality may change with them.

Nothing in the materials records a check of how far the ranking by centrality moves when the coefficient is changed. It reads as though no sensitivity analysis was carried out.

Whether the edge weights were actually used in computing betweenness centrality cannot be settled from the materials

The R script at the end of the dissertation (Appendix 16) supplies as edge values the reciprocal of equation (1) multiplied by 10000, and then calls be <- betweenness(s3, rescale = TRUE). The betweenness function of sna switches by argument between using and not using the edge values, but the script carries no such specification. Moreover, the values printed in Table 6-3 (maximum 631.667) are on a different scale from the output of rescale = TRUE, so the table’s values are presumably obtained from a different call.

In other words, whether the betweenness centrality of Table 6-3 rests on weighted shortest paths or on the presence and absence of edges alone cannot be determined from the materials. If the latter, then the treatment of elevation discussed in the previous section tells on the drawing of the network figure (edge thickness and node colour) but not on the centrality values themselves. This is left standing as a point the original materials do not settle.

The vertices are few, and the values at the endpoints stick at 0

The graph has 44 vertices. Of these, four points — Takakura Pass, Kadonyū, Okudani and Midori Saikōji — have a betweenness centrality of 0.000. They lie at the edge of the graph, where no shortest path between any other pair of vertices could pass. A value of 0 is not evidence of extreme isolation; it is also a consequence of having ended up at the edge through how the data were cut out. That is why the presentation materials exclude Kadonyū from the discussion.

When the vertices are few, adding or removing a single edge can move the ranking by centrality substantially. Reading edges off a figure of the circuit route involves judgement, and since “settlements not included in the circuit route” appear among the dissertation’s stated tasks, the vertex set is not something settled. It is hard to see any meaning in comparing the decimal places of individual values. That the text keeps its reading at the coarse grain of “relatively low” and “relatively high” answers to this state of affairs.

A coincidence is a correlation, not a cause

The settlements low in betweenness centrality coincided with the settlements that come out as outliers in the data on custom. This is an observation that 3 of 8 settlements overlap, and the materials show no trace of any statistical test having been performed. At this number of vertices, one can hardly expect the power to rule out a chance coincidence.

The dissertation does not claim causation either. It is written as “suggests the possibility that each phenomenon is constrained by geographical conditions”, and it states outright that “there is no evidence that the change that occurred here was change through contact”. The discussion further sets side by side a reading that takes change to be fundamentally change through contact and one that takes it to be internal change, without deciding which is right.

The caveat “one cannot rush to a conclusion” in the 2012 presentation materials points the same way. What can be said from this coincidence is no more than that the hypothesis that traffic conditions bear on both language and folklore was not refuted.

On the linguistic side there are data for only five of the eight settlements

Betweenness centrality is computed for all 44 points, but the accent data it is set against exist for only five of the eight settlements of Tokuyama Village. The dissertation writes: “the places are, of the eight settlements of Tokuyama Village, the five settlements of Hongō, Kadonyū, Hazehara, Tsuka and Tonyū”. For Yamate, Kami-Kaiden and Shimo-Kaiden there is no accent record of their own.

Furthermore, only three systems — Hongō, Tsuka and Tonyū — have their types given in Table 6-1. “Kadonyū and Hazehara, which are among the survey area, do not appear in the table because they have the same accent system as Hongō”, it is stated. That Hongō, Hazehara and Kadonyū line up at a linguistic distance of 0.113 in Table 6-4 is therefore not the result of three independent measurements agreeing, but a consequence of Sugito’s report having treated the three as a single system.

The discussion contains the passage “that Hazehara, Yamate, Hongō, Kami-Kaiden and Shimo-Kaiden show equal values in linguistic distance irrespective of their geographical distance is surmised to be due to a working other than geographical factors, for example traffic volume”; but for Yamate, Kami-Kaiden and Shimo-Kaiden among these, no underlying accent record is to be found in Tables 6-1 and 6-4. Which data this passage rests on cannot be judged from the materials at hand.

The attribution of the source material is inconsistent

As to the source of the circuit route, the 2012 presentation materials give “the early-modern circuit route of priests from Jōshōji (Tokuyama Village History Editorial Committee 1973), Figure 2”, while the dissertation gives “the early-modern circuit route of Jōshōji recorded in the emergency survey report on folklore materials [Gifu Prefectural Board of Education, 1973] (Figure 6-1)”. Which of the two works the figure used is taken from, or whether the same figure is contained in both, cannot be judged from the materials at hand. Both works appear in the reference list.

This method looks at no linguistic data whatever

Finally, an obvious but important point. What went into the computation of betweenness centrality is the figure of the circuit route and the latitude, longitude and elevation of each point — nothing else. Neither accent nor custom enters. Which is precisely why the coincidence with the linguistic data means something: that is the design of the analysis.

Put the other way round, this number says nothing about language. “Tonyū is low in betweenness centrality” is a property of the traffic network; “the accent of Tonyū is isolated” is a property of the language. What joins them is interpretation, not computation. Mixing the two and saying “betweenness centrality measures linguistic isolation” destroys the point of this analysis, which is that it sets two independent measurements against each other.