The correspondence network of Adriaan Reland (with data taken from Early Modern Letters Online) as a ego network taken to 2.5 degrees
Friday n° 37, June 28th, 2019
The last
weeks have been packed with work, so that my last two blog posts had to be
cancelled because I had to write chapters, presentations, papers, and other
things (all about or issuing from the project, so that has all been working
time) and was not able to communicate the state of work here for the time
being. As promised, I am now returning to my schedule as the flood begins to
sink and I’m no longer fearing to drown any moment, and will from now on again
deliver my weekly research stats.
Hooray for
data!
And to begin this week’s state of research, let me take the opportunity to advertise the ‘other thing’ I have been working at for the past weeks, which actually is a data set. Thanks to and in collaboration with the ERC Skillnet project I have been able to publish some of the letters I’ve been working as ‘The correspondence of Adriaan Reland’ on Early Modern Letters Online. 212 letters have either survived or can be inferred from those letters which I close-read with certainty, and, sadly, that’s all that is left. The metadata of these letters to and from Reland are now accessible via this collection, so I’d like to invite you all over to have a look at these. The added value of embedding them in a larger context as provided by EMLO of course lays in the possibility to explore the wider interconnections of this parcel of letters within the res publica litterarum of Reland’s time, so I thought, let’s give that a try for today.
A 2 degree Ego
network
The 212
Reland letters have been sent to 36 correspondents, not so many in terms of
scholarly correspondences, so it seemed a good idea to construct a second
degree ego network from this in EMLO terms: I checked all of Reland’s direct
correspondents via EMLO for their contacts among each other, to see how densely
they were interconnected apart from their shared correspondence with Reland. So
what you see in this visualization of the whole network is Adriaan Reland at
the centre, highlighted in red, as befits a good ego network, and gathered
around him his direct correspondents as green nodes, with the communication to Reland
as green arrows also. The thickness of the edges depends on the amount of
letters exchanged, whereas the size of the nodes is due to the total number of
references to the scholar the node represents in terms of the whole network. Connections
between Reland’s direct correspondents drawn from EMLO are visualized by black
arrows, the thickness again keyed to the number of letters.
The missing
0.5 degrees…
But first
of all there is a lot of blue and grey stuff in this diagram which I have not
yet said anything about, and second I promised you a 2.5 degree network in the
opening headline. So what about that?
Well, as
you suspect already, both things are directly related. To start with the
missing 0.5 degrees, this was due to the way in which I collected data on these
letters. As my project is all about references to other scholars to track the
circulation of information, I went through a part of these letters very
closely, trying to identify each person and publication mentioned therein. Now
EMLO does not support inclosing information on publications in their metadata
on the letters, but they do support inclosing mentions of persons, so this is
all in there. And that means these data were there to work with them in drawing
up the ego network. So what I wanted to have a look at was if the people
mentioned to Reland’s direct correspondents would line up with the rest of the
network – that is, the contemporary people mentioned. That would give an
indication as to whether this is something like an 18th century communication
bubble and thus might provide a way to reconstruct missing epistolary evidence.
All of these mentions I took to constitute a triad between a) the person who
mentions a name, b) the person who is mentioned, and c) the person this name is
mentioned to, and all of these relations are visualized in grey within this
diagram, as they quite literally are somewhat shady in terms of ‘real’ network
edges.
Click the image for a full view of the visualization graph.
What I then
did was checking in EMLO if those people who were only mentioned in Reland’s
direct correspondences had direct contacts with his correspondents or amongst
each other. This would be something in between a real third-degree connection
and a second-degree connection, so I decided to label it 2.5 degrees of
separation. For those people and connections who had such connections, nodes
and edges are coloured in blue to clearly distinguish them from the green nodes
of the inner circle of direct correspondents and the green and black relations
of these with Reland and amongst each other.
… and what
they revealed
What’s
really of interest now is of course: What did I gain from doing this? Is there
anything new for my project in there? And yes, it was. There are 116 people
mentioned in the letters between Reland and his correspondents, 97 out of which
still lived in 1680, the year which I took as the point of demarcation between
roughly ‘contemporary’ scholars and those whose correspondences I did not take
to be relevant to Reland’s connectedness within the republic of letters in any
way (this starting point is of course debatable, but one has to start somewhere).
This testifies to Reland’s letters discussing more recent issues then debating past
works and results; quite a large share of these 97 scholars mentioned whom I
designated as ‘contemporary’ actually survived him, sometimes for several
decades.
Of the 97
contemporaries mentioned, 26 had contacts either amongst each other –
represented by blue arrows – or with members of the green inner circle of
correspondents, represented by black arrows. Together with the interconnections
of Reland’s direct correspondents between themselves, the second degree of the
Ego network, the second-and-a-half-degree connections make clear that he
actually was situated in an environment where most people directly or
indirectly knew each other, and much of what he relates to in his letters has
to be seen in this context. Although these people were spread out across the
Netherlands, France, Britain, the Holy Roman Empire, Italy, and Denmark, it
seems that they formed a remarkably tight-knit community. If this was a
strength or a weakness of the network in question would have to be evaluated
against contextual information which EMLO does not provide, but it gives hints
where to look next.
Mind the
gap!
All I’ve written in this post so far has to be taken with a grain of salt, of course, because EMLO is – as great and wonderful a resource as it is – far from being complete (although I would think it is comprehensive). This means that most probably there are interconnections which I missed out on because they are not (yet) in there. And this becomes even more pronounced as I did not close-read all of Reland’s remaining letters but only about a third of them, so I have missed out on a lot of mentions which would have given me new leads to track in EMLO as well. From the point of a study of remembrance and forgetting such as mine this is of course something to emphasize: What is in there is what is still – at least in some way – in circulation, in this case triggered by current research into these phenomena; and the gaps are caused by processes of discarding and source loss, which are parts of structural forgetting. So by mapping out the gaps, I do get a better grip on what I am really at also. And it’s never bad to gain added benefits from something.
And: Mind
the results nevertheless!
But the point was precisely this: To see what I could do with this resource even as it stands now and regardless of the patchiness of my own research so far. And that proved quite a success, because in all likelihood I would only have ended up with more connections in the end, not less, which strengthens my initial hypothesis that the 2.5 degrees are a useful way of coming to terms with gaps in the physical evidence. In Reland’s case, this worked out well and points to him as really being closely connected within a certain epistemic community (as I once termed this) of his day.
What now
remains to be done is to see if this also works out for my other three
protagonists, since this would provide a way to cope with the dearth of direct
epistolary evidence. I’ll see to it that I can present some preliminary results
from going in this direction during the coming weeks.
PS: Actually, it’s a funny coincidence that today is not only the 37th Friday of my project but also my 37th birthday. Makes it feel even better to be back on track again. And now I’m off for some cake. See you next Friday!
Snippet from the Acta Eruditorum, June 1711 issue, p. 269.
Friday n° 29, April 25th, 2019
If being
remembered or forgotten is a function of reference frequency, of circulating
information, an obvious conclusion seems to be that if you want to be
remembered, you yourself should start circulating information lest you get
forgotten. In scholarly contexts, this basically means spreading the word about
what one is doing or has produced. This might in turn trigger references to you
and your publications, discoveries, theories or other achievements which in
turn might provide starting points for other references. Self-advertisement,
for this and other, more directly visible reasons, has been and is part and
parcel of academic communication. In network analysis, the reasons why such
attempts at self-promotion were successful or not is often explained or even
predicted by the structural features of the individual’s networks.
Shadowy
networks
But what
about the networks we are only partially able to reconstruct because of source
loss? In some cases, I know that there were connections but can’t say much more
about depth and nature of these connections because the source documents
necessary to judge this have been lost. Any network reconstructed under such
circumstances will be distorted, because the parts of it traces of which have
survived as documents will be privileged over those parts where this is not the
case. So what to do with the parts of the network which can only be traced as
shadows, as ghosts of nodes and edges that once were?
Self-advertisement,
done successfully
Let me
start with a small piece of circumstantial evidence with throws one such ghost
edge in my network of letters into sharper relief. In June 1711, the Acta Eruditorum published a small piece
of seven pages titled “On the manuscript commentary of Blessed Jerome which
exists in the library of Marcus Meibom in Amsterdam”.[1]
Most of the text was composed of excerpts from the manuscript in question, but
ahead of this the editorial board of the Acta
Eruditorum lost a few words on how they got the paper in form of a short
introduction:
“Lately the illustrious Adriaan Reland whom we already have given honourable mention in these Acta more than once has sent us some excerpts from a manuscript commentary on Job by [St.] Jerome, whishing them to be included in our Acta with the intention that scholars may by this specimen pass judgment on whether it is a genuine work by Jerome or not.”[2]
[Mencke]: De b[eati] Hieronymi commentario m[anu]s[cri]pto in Jobum, AE 30, June 1711, p. 269.
This
passage now not only fits in quite well with my overall framework of references
and their valorisation in scholarly circles. It also explicitly states what I –
based on studies such as that of Huub Laeven on the networks of Otto Mencke
(1644–1707) and his son Johann Burchard Mencke (1674–1732), the successive
editors of the Acta Eruditorum[3]
– already had suspected: that either Mencke sr. or jr., or both, were in direct
correspondence with Reland. Until now I just had no tangible evidence for such
a connection, as the letters of all parties involved, Otto Mencke, Johann Burchard
Mencke, and Adriaan Reland, have only fragmentarily survived. The letter
concerning the codex containing the work in question here, the commentary on
the Old Testament book of Job supposedly written by St. Jerome, the church
father, does not exist anymore (at least not to my knowledge). But the easiest
way to account for the passage just quoted is to assume that it indeed did
exist.
Ghost edges
As glad as
I am to finally have made sure that this particular ghost edge really existed, I
am nevertheless aware that the basic problem context underlying this discovery
has just become a bit more serious at the same time.
For on the one hand some of his surviving letters already point to Reland being a conscious and very active self-promoter who had a keen eye and good hand in picking opportunities to distribute his publications, and to this another distribution channel – that of the Acta Eruditorum – has just been added now. As there are quite a few “honourable mentions” of Reland by the Acta Eruditorum, like Johann Burchard Mencke wrote (or let write: as leading editor he has to be held responsible for anonymous texts in his journal), this prompts the question of how they were caused in the first place. As there are at least two letters by Reland to Jean-Paul Bignon (1662–1743), editor of the Journal des Savants in Paris, which deal with Reland sending Bignon his publications for distributing them amongst his French connections including review copies,[4] there is no reason to assume that something similar might not have taken place in his correspondence with the leading German scholarly journal as well as with its French model. This might seem to be supported by the rising reference frequency in the Acta Eruditorum concerning Reland between 1701 and 1711:
(Only the text pieces containing references to Reland are counted, not the total of references.)
The upward trend visible here might be taken as just the depiction of a young scholar’s rise of fame while making his way through academia. Reland had been awarded his first professorial post in Harderwijk in 1698/99, only to move to a more prestigious chair at Utrecht in 1700/01, publishing continuously. Or it might be an illustration of a correspondence successfully feeding the editorial board at Leipzig with relevant news and thus ensuring continuous reference to oneself. As I cannot say much more about the ghost edge than that it existed, but not for how long and how intensively it was used, the question has to remain open for now.
And on the other hand, the fragmentary state of the Reland correspondence has by now turned up quite a handful of such connections where there are either indications of direct correspondence and no surviving letters or one or two letters surviving, indicative of a communication channel which must originally have accommodated many letters more. As I already pointed out in one of my earlier posts, the correspondence between Mathurin Veyssière de la Croze (1661–1739) and Reland is only documented by three letters, all of which are no longer extant in the original. Given the close intersection of research interests between the two of them it is highly unlikely that there were not much more originally; but how could this be translated into a meaningful part of a network? The same is true for Johann Baptist Ott (1661–1744) the communication between whom and Reland is only evidenced by one printed letter in Reland’s second treatise on the Samaritan coins, as I pointed out here. It is also true for Marcus Meibom (1630–1711), the scholar whose manuscript was the reason for the note in the Acta Eruditorum which caused me to write this post in the first place. It is even true for another of my protagonists, Johannes Braun, as there are a few letters between him and Reland still extant but the bulk of Braun’s correspondence is also lost. This is by far no complete list, but I am determined to draw one up as far as this will be possible.
The
Chicken-and-Egg of Loss, Forgetting, and References
The
question posed by ghost edges is of course how they relate to forgetting. They
are clearly indicative of structural forgetting taking place, but in which way?
Their presence could be seen as a natural effect of processes of structural forgetting:
As someone fades from structural remembrance, his papers or letters become
devalued and thus more likely to be sold off, discarded, or altogether lost.
But their presence could also be the cause rather than the effect of becoming
forgotten: As the papers and letters of someone become sold off, were
discarded, or otherwise lost, materials are removed from the archival record
which might have triggered new references had they still been there, which in
turn leads to a drop in reference frequency and thus to structural forgetting.
This is a new variant of the ages-old chicken-and-egg problem, so I have go to
searching for additional factor which might help me figuring out if a
particular shadowy part of the network is a ghost edge chicken or a ghost edge
egg.
[1] [Johann Burchard Mencke]: De
b[eati] Hieronymi commentario m[anu]s[cri]pto in Jobum, qui Amstelodami in Bibliotheca
Marci Meibomii exstat, in: Acta Eruditorum 30, June 1711, pp. 269-275.
[2] Ibid, p. 269: „Misit nuper ad nos
Vir Cl. Hadrianus Relandus, cujus non semel honorificam in his Actis fecimus
mentionem, Excerpta quaedam ex Commentario MS. Hieronymi in Jobum, eaque Actis
nostris inseri cupivit eo consilio, ut eruditis hoc e specimine iudicandi copia
fieret, sitne is genuinus Hieronymi foetus nec ne.”
[3] Cf. Huub Laeven: Otto Mencke
(1644–1707): The Outlines of his Network of Correspondents, in: C.
Berkvens-Stevelinck, H. Bots, J. Häseler (eds.): Les grands intermédiaires
culturels de la république des lettres. Études de réseaux de correspondances du XVIe au XVIIIe siècles, Paris:
Champion 2005, pp. 229–256 ; —: “Dies ist wol ohne Streit die größte
unter denen Holländischen Public-Bibliotheken“. Johann Burkhard Mencke’s
bezoek aan Leiden in 1698, in: Omslag. Bulletin van de Universiteitsbibliotheek
Leiden en het Scaliger Instituut 4, 1/2006, pp. 1–3.
[4] UB Leiden BPL 885 – 052
(Rabault-Risseeuw): Adriaan Reland to Jean-Paul Bignon, Utrecht 13 June 1714
(19th century copy), and KB Den Haag 72 D 37, 11 A: Adriaan Reland to Jean-Paul
Bignon, 23 June 1714.
Snippet of the network visualization for the 502 publication sample described in this post; mind the prominent position of Reland’s “Palaestina Illustrata” (big green dot left on top) and the unconnected component in the lower right corner.
… Adrien Reland’s 1714 Palaestina ex monumentis veteribus illustrata!
And so the winner is me, too, for I guessed it correctly.
A two weeks’ post
But one
thing after the other. First, the date: this is my blog post for
Saturday, March 9th, 2019, for Friday
no. 22;
I seem to
acquire a bad habit of posting on Saturdays rather than Fridays. For today, my
excuses are, in chronological order, a) I had to help out at my son’s school,
fixing some shelves; b) I had to figure out how to clear some financial matters
regarding how to pay my salary from this project in a way that some of it
actually ends up with me in the end; c) my youngest daughter stubbornly refused
to go to sleep this evening. Obviously I am not very good at scheduling my home
office work hours, for although I started out at 8:00 in the morning, by 21:30
I had got down to a meagre seven hours of working time. And d) I made a tiny
configuring mistake, messed up my calculations, and had to start all over
again, ruining some two hours of work. I suspect I better had not started
calculating only at 21:30, but a), b), and c) forced me to.
Going for
some metrics, step 1: Gathering data
But the calculations are crucial, because that’s what I originally intended to show you. As I announced in my last post, I now have finished three-quarters of my projected sample of scholarly journals, which has taken me two weeks to complete, clean, and analyse now.
That is to say, I have gone through the digitized versions of the Journal des Savants, the Philosophical Transactions, and the Maandelyke uittreksels, of Boekzaal der geleerde waerelt (more info here), between 1700 and 1799. I have added all issues of these journals referencing one of my four protagonists in any way to my database. In numbers, this means 117 issues of the Journal des Savants, 9 of the Philosophical Transactions (yes, only nine, but I have already argued they are somewhat special here), and 89 of the Maandelyke uittreksels – or 205 journal issues in total. In going through these issues I have examined each page on which at least one of my protagonists was referenced, identified all other scholars and all publications on that page, and stored these data, too, as a basis for co-citation analysis to identify perceived epistemic communities and their changes over time. This netted me another 287 quoted publications, and another 739 scholars referred to and/or connected to quoted publications (as authors, editors, translators etc.). I must confess that I am a bit proud of having managed to completely identify close to 690 of these, or more than 90%. But today everything will be about publications, so the really interesting figure is that of 502 publications in this sample.
Going for
some metrics, step 2: Setting a framework for analysis
The problem
that I now got was how to deal with these data. Plain visualizing did not work
out anymore to really map out the intriguing details. So it needed to be done
the rough way, by calculating metrics for the sample, hoping for something
interesting to turn up. The visualizations did help me, in the way of pointing
out which ways to structure the relations to be investigated would likely not
yield good results. I first thought I might try something like mapping ‘shared
contributors’, that is, connecting publications by way of the same scholars
contributing to them (as authors, editors, or translators). This turned out to
be pretty useless because it only favoured large edited collections who
assembled texts from many different authors. And that’s the reason why this
post is not about persons but publications only; the real co-citation analysis
still has to wait for a bit. So it seemed better to bypass persons for the time
being and only to link publications to publications, and I did so by way of
quotations, that is, two publications are seen as connected if at least one of
them quotes the other. That brought some interesting results about.
Going for
some metrics, step 3: Finally going for metrics!
With the framework set up to network this publication sample, it was high time (half past nine already!) to start calculating metrics. To facilitate calculation, I started with assuming the network edges to be undirected, that is, a link from publication A via a quote in A to publication B works both ways, from A to B and from B to A. I know that this might be a questionable simplification; but as this may be tested by comparison, I will set this matter aside for a rainy day when I don’t have any idea what to write in this blog for the week to have the opportunity to at least redo these calculations for directed edges. (And as I once started tracking time in this post, it is now 4:00 in the morning and high time that I get to bed to have at least some sleep. I’ll continue around noon.) Moreover, as the structure of connections within what one takes to be a network depends on what the question is, and I am interesting in tracing perceived epistemic communities here – that is, publications seen as belonging to shared domains of knowledge – edge directionality is less important than it might be for other questions to ask. (This is a piece of midnight reasoning, but it still looks sound now at 10:30 on the day after.) I could as well also have collapsed the journals into edges connecting the rest of the publications to more explicitly claim this, but I wanted to also get an impression of the position of the individual journal issues, and so I kept them as nodes. Admittedly, this model does have the drawback that relying on quotations only provides only a quite simplified picture of the interconnections structuring domains of knowledge, but it should serve to give a good first impression of the sample’s general structure. Having sample and model settled, I used the opportunity to test Nodegoat’s analysis functions and calculated some metrics.
A lot of
numbers
To keep the
scores comparable across different metrics, I chose to normalize them where
possible. A short look at the visualization (see header for larger picture)
made clear what was to be expected: the network is disconnected. Not all publications
are referred to as situated in overlapping domains of knowledge; some are
distinctly separate from the rest. This is important here because it directly
impacts the calculations of the closeness metric. Closeness serves to indicate
how close any given node is to all other nodes in the network. In mapping out
shared domains of knowledge this might be quite interesting, as nodes with low
closeness scores might be supposed to partake of many fields at once being
referenced in differing contexts, and thus be important to look at. But
closeness measures path lengths to calculate the average distance from node X
to all other nodes, and this does not work in disconnected networks (because
two nodes between which there is no path would be at undefined = infinite
distance from each other). Nodegoat provides a workaround to that by
substituting a maximum distance for path length between unconnected nodes, this maximum
being equal to the total number of nodes in the network.[1]
First:
Betweenness
The first
measure I calculated was betweenness[2]
(because of the problems with closeness). Betweenness works on disconnected
networks and thus was the obvious first choice. Roughly put, betweenness serves
to indicate whether a certain node may be considered a gatekeeper, that is, if
it is situated at a vital connection point in the network. In assuming an
undirected graph, for mapping shared domains of knowledge this resembles
closeness: it should point to publications situated at the intersection of
several domains, and thus of potential importance for each of these. I must
qualify this as ‘potential importance’ because only being situated between
different fields of knowledge does not equal making important contributions to
any of these fields; this will have to be cross-checked with other metrics,
then.
Top 10
Betweenness
These are
the top ten results in terms of betweenness for the whole of the network:
And those are the respective results for the top-scoring publications of/connected to:
Adrien Reland, by Betweenness
Eusèbe Renaudot, by Betweenness
Johannes Braun, by Betweenness
Thomas Gale, by Betweenness
What
becomes directly apparent is that there are a lot Reland’s publications in the
network, not only on vital connection points but also in total. In fact, 37 out
of 287 non-journal publications have Reland as their main author/editor, or
12,9 %; the number does matter because I only added publications to this sample
when coming across a quotation within the sample. Compared to 2.8 % for Eusebè
Renaudot (8 publications), 1.7 % for Johannes Braun (5 publications), and 1.4 %
for Thomas Gale (4 publications) this looks even more impressive. But a large
output as such does not tell anything about the quality or the reception of
that output. There also is one publication by Eusebè Renaudot among the top ten
in betweenness, too.
Second:
Closeness
As already said, the closeness scores for this sample are to be taken with a grain of salt because of the disconnectedness workaround implemented in Nodegoat. But the prediction I theoretically made when thinking about betweenness in this network – that it would line up quite closely with closeness because pointing to structurally similar positions within the network – did come true in looking at the results for closeness, so I am tempted to regard these results as usefull still. Important: The first score in the “A” for Analysis column is always the one discussed!
Top 10 by Closeness
The top ten
publications of the network in terms of closeness scores are:
This again
underscores the relevance of Reland’s publications within the network as a
whole, and especially of his Palaestina
Illustrata.
And those are the respective results for the top-scoring publications of/connected to:
Adrien Reland, by Closeness
Eusèbe Renaudot, by Closeness
Johannes Braun, by Closeness
Thomas Gale, by Closeness
Third:
Degree
In
undirected graphs such as this, Degree just counts the number of connections
any given node in the network has. To be precise, Nodegoat counts the number of
all edges starting from and ending at any given node, allowing for duplicates
edges, thus producing high scores on average.[3]
For an analysis of shared domains of knowledge as proposed here Degree should
be relevant as a corrective. Whereas Betweenness and Closeness both point to
structural positions of publications in regard to their location between
domains of knowledge, Degree points to the importance of a given publication at
this structural position. Or, to put it more precisely, to the attention
generated by the publication in question, as I am focusing on quotations made
by scholarly journals to this publication; and many such quotations do not
necessarily point to the scholarly but in any case to the public impact a work
made.
Top 10 by
Degree
Looking at the Degree scores from this perspective makes clear that while Reland’s publications might share in more domains of knowledge, within their respective domains Renaudot’s publications obviously attracted comparable attention. And looking at the respective results for the top-scoring publications of/connected to Johannes Braun and Thomas Gale in comparison makes clear that they were not only tied more closely to special domains of knowledge but also attracted less attention by the journals in question, perhaps because of this more stringent specialisation. So here are the Degree scores for publications divided by individuals:
Adrien Reland, by Degree
Eusèbe Renaudot, by Degree
Johannes Braun, by Degree
Thomas Gale, by Degree
A cautionary note: It does not pay to put too much trust in Degree scores, because they tend to push publications situated within certain reference patterns. Consider the example of Mathurin Veyssière de la Croze’s Lexicon aegyptiaco-latinum, the Coptic dictionary edited and published by Karl Gottfried Woide in 1775 which has already featured in one of my posts.
With a Degree of 33 it scores shortly below a top 10 place in Degree which, following the reasoning laid out above, should indicate its importance for its particular domain(s) of knowledge – it attracted a lot of attention, because it has a lot of quotes. But all of these quotes are in fact derived from one singe journal issue, the June 1774 issue, part one, of the Journal des Savants, as becomes visible from the cross-references section of its database entry.
And there
it assembles all of these quotes because it features in many different respects
in the announcement written by Woide himself to highlight his upcoming
publication, which makes the reference section of this piece look a bit monothematic:
Snippet from the references contained in Woide’s publication announcement
So while
Degree may be taken as an indicator of importance within a given field by
capturing public attention, this is easily manipulated, and has to be
cross-checked against another metric for validation.
Fourth:
Pagerank
Nodegoat
allows for calculating Pagerank scores, following the original Google
algorithm. As Pagerank was originally invented to determine the relative
importance of information sources (in this case, websites) in a network through
which a user might randomly move, this model might also be applied to domains
of knowledge in a web of publications, treating quotations as paper-borne
hyperlinks. Random movement through the graph is facilitated by its
undirectedness, so please keep in mind that modelling it as undirected may be a
questionable decision, and don’t trust these metric too much. The good thing
about Pagerank is that allows for determining both the relative importance of quoted
publications and of quoting journals in this particular configuration, so I
would like to use it to counterbalance the shortcomings of Degree pointed out
above. In running Pagerank, Woide/la Croze’s dictionary disappears from the
leading places all of a sudden, so this seems to work. The top publications
according to Pagerank thus are:
Top 10 by
Pagerank
Surprise, surprise:
The main hubs for distributing quotes – and thus sorting domains of knowledge –
are journals! Makes me almost wonder why I chose to go by them in the first
place… But more interesting in here is that there one publication from the 287
quoted works in the sample which managed to get a place in the top 10, and that
is – surprise again! – Reland’s Palaestina
Illustrata. This in turn is due by it being quoted by a number of journal
issues (from all three journal series) which are themselves important quotation
hubs, as becomes evident when looking at the cross-references to Palaestina Illustrata, that is, the
publications in the sample linking to it.
This looks
as if Pagerank indeed might be a good tool to determine the importance of a
publication at its respective structural position, at best in combination with
Degree (and Palaestina Illustrata
scores high on both). So what about the top scores for the rest of the field?
Adrien Reland, by Pagerank
Eusèbe Renaudot, by Pagerank
Johannes Braun, by Pagerank
Thomas Gale, by Pagerank
Combining
metrics
Well, that was a lot of tables, numbers, and scores. Well done! Only a few more to go. Now the last thing to do is to find a way to purposefully combine the different metrics results assembled so far to draw something relating to my larger research question from it. To do so, I ventured for a first try to identify the top 5 publications of each of my protagonists by comparison of the results I presented above. This yielded the following table[4]:
Top 5 by:
Betweenness
Closeness
Pagerank
Degree
Reland
Palaestina ex
monumentis veteribus illustrata
Palaestina ex
monumentis veteribus illustrata
Palaestina ex
monumentis veteribus illustrata
Palaestina ex
monumentis veteribus illustrata
Reland
De nummis veteris Hebraeorum
De nummis veteris Hebraeorum
Antiquitates
sacrae vet. Hebr. (4th ed.)
De nummis veteris Hebraeorum
Reland
De religione mohammedica
De religione mohammedica
Antiquitates sacrae veterum Hebraeorum
De religione mohammedica
Reland
Antiquitates sacrae veterum Hebraeorum
Antiquitates sacrae veterum Hebraeorum
Verhandeling van de godsdienst
Antiquitates sacrae veterum Hebraeorum
Reland
Encheiridion studiosi
Dissertationum Miscellanearum
Oratio de galli cantu
Hierosolymae
Decas exercitationum […] nomine Jehovae
Braun
Commentarius in
epistolam ad Hebraeos
Commentarius in
epistolam ad Hebraeos
Leere der verbonden (4th ed.)
Doctrina foederum
Braun
Leere der verbonden (4th ed.)
Vestitus sacerdotum Hebraeorum
Avertissement necessaire aux eglises
Leere der verbonden (4th ed.)
Braun
Avertissement necessaire aux eglises
Doctrina foederum
Commentarius in
epistolam ad Hebraeos
Commentarius in
epistolam ad Hebraeos
Braun
Doctrina foederum
Avertissement necessaire aux eglises
Vestitus sacerdotum Hebraeorum
Avertissement necessaire aux eglises
Braun
Vestitus sacerdotum Hebraeorum
Leere der verbonden (4th ed.)
Doctrina foederum
Vestitus sacerdotum Hebraeorum
Renaudot
Historia patriarcharum Alexandrinorum
Historia patriarcharum Alexandrinorum
Liturgiarum Orientalium Collectio
Liturgiarum Orientalium Collectio
Renaudot
La perpetuité de la
foy, 4
Liturgiarum Orientalium Collectio
La perpetuité de la
foy, 4
Defense de
l'”histoire des patriaches”
Renaudot
Liturgiarum Orientalium Collectio
La perpetuité de la
foy, 4
Anciennes relationes des Indes
Anciennes relationes des Indes
Renaudot
La perpetuité de la
foy, 5
La perpetuité de la
foy, 5
La perpetuité de la
foy, 5
La perpetuité de la
foy, 4
Renaudot
Anciennes relationes des Indes
Anciennes relationes des Indes
Historia patriarcharum Alexandrinorum
Genadii patriarchi homiliae
Gale
Antonini iter Britanniarum commentarius
Antonini iter Britanniarum commentarius
Antonini iter Britanniarum commentarius
Antonini iter Britanniarum commentarius
Gale
Jamblichii de mysteriis liber
Jamblichii de mysteriis liber
Historiae poeticae scriptores antiqui
Historiae Anglicanae scriptores V.2
Gale
Historiae Anglicanae scriptores V.2
Historiae poeticae scriptores antiqui
Historiae Anglicanae scriptores V.2
Historiae poeticae scriptores antiqui
Gale
Historiae poeticae scriptores antiqui
Historiae Anglicanae scriptores V.2
Jamblichii de mysteriis liber
Jamblichii de mysteriis liber
Creating a
Shortest Path Matrix
To fuse
this into something more informative I thought I might utilize a special
function of Nodegoat’s, and that is its ability to calculate shortest paths
between given selections of nodes. In this case, this meant that I first
settled on a matrix of four times four publications: The top 4 publications
after comparing the scores of all metrics for each of my four protagonists. I
chose to use the top four because only four of Gale’s publications made it into
the sample, and this provides better comparability then. Now I used the
Shortest Path function to calculate the length of the shortest path through
this network from each of these publications to each other, and set the results
down in form of a matrix.[5]
It looks like this.
Conclusions
What does
this tell me now? Well, first of all it highlights the isolated position of
some of these publications, which obviously do not share domains of knowledge
with others; this is true for the five marked with grey lines which have no
connections to the rest of the matrix. It moreover points to the broader
diversity of Reland’s publications compared to the rest of the network: His
four publications all have connections within the matrix, while for Renaudot
one publication does not and for Braun and Gale two publications each. Reland’s
and Renaudot’s oeuvres and positions are similar in that both are internally
coherent – the smallest paths to those of their own publications connected to
the rest of the matrix are two each – and well-connected: their publications
are not only connected to more of the rest of the matrix, they are also
connected by shorter paths, making their works appear to be more central. Braun
and Gale on the other hand are similar in having less many publications connected
to the rest of the matrix, and in those publications being situated in strongly
differing fields, as indicated by their larger internal distance from each
other compared to Reland and Renaudot. And both of them are on the outskirts of
the network rather than in the centre as indicated by the long shortest paths
to other publications in the matrix.
This buttresses the claims I have brought forward based on other impressions already: That Reland and Renaudot form a comparable pair of actors, as Gale and Braun do; and that Reland seems to be the most versatile of all four, which might be the reason why he was the last of the four to get forgotten. And, as I already suspected last week, that his Palaestina Illustrata might be more relevant for this process than his other works, even if they are better known today (as his 1705 De religione mohammedica for instance).
But this
has been a fairly static picture of a phenomenon spanning one century, so the
next task will be to dynamize it. Work to do!
[1] So in looking at the closeness
scores in the following, always keep in mind that the maximum path length taken
into consideration is 502.
[2] With duplicated edges taken
into account and weighted according to distance, that is, duplicates add edge
length.
[3] And Nodegoat does not automatically
normalize Degree centrality. But this is an easy operation: If you want to do
so, just divide any absolute Degree score by the total number of edges in the
network, in this case, 2577.
[4] Publications marked in red only
appear once in the table and are therefore discounted from further comparison.
[5] Please keep in mind that shortest paths are elongated in my setting because two quoted publications A and B are (almost) always connected via a journal in between, so the usual shortest path possible between A and B is two links (A –link one– Journal –link two– B).