Investigating the case of the Investiture Struggle in the diocese of Cambrai–Arras (c. 1100), this article aims at exploring some crucial issues for historians using social network analysis in the study of heterogeneous relationships. The study proceeds along three lines of enquiry. First, by establishing a hierarchy in the different types of relationships mentioned in the sources, it determines which of them are the most important to model and understand the structure of the network. Second, it demonstrates it is unnecessary to consider co-witnessing relationships (i.e. to be witnesses of a same charter) in the modelling of networks. Indeed, co-witnessing relationships do not help to improve our understanding of the structure of the parties at stake in a conflict. Finally, this paper deals with the importance of rank order in the witness lists. It demonstrates that, in the case of Cambrai, rank order does not have an influence on the global structure of the network. In other words, all individuals in the same witness list play a similar role in the network in terms of party structuring.

§1 For a few years now, social network analysis has become a relatively common tool for medievalists working on political history. Following in the footsteps of John Padgett and Christopher K. Ansell on the Medici (

§2 Some difficulties among these are related to the heterogeneity of the set of social and political relations being modelled. Very often, the medieval sources used to construct the analyzed graphs make us aware of a whole range of links between the people mentioned in them, whose natures are multiple and diverse. This observation is particularly true when the basis of the medievalist’s work is a diplomatic corpus consisting in charters describing various legal actions. In this case, the heterogeneity of relations appears at three levels. First, the relationships attested in charters of different legal types are different in nature. For example, the protagonists of a donation charter do not have the same relationship as those of a conflict resolution document. Second, within the same charter, different roles give rise to different relationships. For instance, one could expect that the author-beneficiary link is not identical to the author-witness link. Third, even for equal roles, it is relevant to ask whether the relationships between individuals are quite the same. Does a charter describing the donation of a good to a group of beneficiaries necessarily attest to links between these beneficiaries and the donor that are all equal in intensity?

§3 In this article, we study some methodological issues related to these questions with the help of quantitative methods. To do so, we explore the case of a complex, but “classical”, political conflict occurring in Cambrai towards 1100 in the context of the Gregorian reform. We have chosen this case study because the events have already been studied through a qualitative approach by one of us (

§4 Our methodology is based on a multi-layer network approach. Its main idea is to decompose the considered graph into subgraphs corresponding to different relation types (the “layers”). We can thus consider those layers separately, apply transformations to them, and aggregate them into a new single-layer network. The resulting graph is finally compared to the original undecomposed graph with the help of a procedure that automatically reconstructs the parties of the conflict.

§5 The application of this framework to the Cambresian network allows us to address three methodological issues. First, we ask whether all categories of edges in the graph (i.e., all categories of relationships) appearing in the charters contribute equally to our understanding of the political conflict under study. The interest of obtaining a hierarchy of types of relationships in terms of efficiency in the modelling of a historical phenomenon is twofold. On the one hand, it helps to guide the historian who is building a network on the basis of a diplomatic corpus, indicating which links he should pay particular attention to, etc. On the other hand, such a ranking of socio-political links in order of importance tells us something about the party structure of the Cambrai conflict, and more generally about the nature of interpersonal relations in the Middle Ages.

§6 Second, we look at a particular type of relationship that appears only indirectly in the diplomatic texts: co-witnessing (which we will also call co-subscription). This relationship binds together the witnesses of a same charter, those individuals who appear on the lists copied at the end of the charters and whose function was to validate the legal action inscribed in the act (

§7 Third, we are interested in the relations that the witnesses have with the authors of the charters, and more precisely in the order in which they are mentioned in the list given at the end of the act. According to historiography, this order is not due to chance, and carries a real meaning for medieval men (

§8 Our argument will follow three steps. In the first part of the paper, we will present briefly the political context in which the Investiture Contest in Cambrai occurred. We will also describe the corpora we have used, focusing primarily on the eleventh- and twelfth-century episcopal charters of Cambrai. Then, we will turn to the methodology we have developed to address the difficulties historians have experienced while dealing with medieval relationships heterogeneity. Finally, we will present our results, by focusing first on the automatic labelling of the parties, then on the answers we propose to the three questions asked here above.

§9 In the last few years, French historiography has underlined the role of the Gregorian reform in the transformation of society in the high Middle Ages. According to Florian Mazel, the Gregorian reform was a “global revolution” by which not only the political structures but also the mentalities were transformed (

§10 The conflict that devastated the county of Cambrai at the turn of the eleventh and twelfth centuries is known through three types of sources: a) The numerous charters issued by Bishops Walcher, Manasses and Odo of Cambrai (

§11 In order to analyse the struggle, we have reconstructed the ego (or personal) networks of the three bishops claiming the episcopal see of Cambrai. Therefore, it was necessary to gather all the charters produced in their name (an example of which is shown in

One of the charters under consideration. The witness list follows the capital S in the bottom half of the page (

§12 We will only use the two other sources that are informative about the Investiture Contest in comparison with the charters, as explained at the end of the previous section. One of the best sources of information about the conflict is the

§13 The “Register” of Bishop Lambert of Arras gives a complementary image of the conflict. The term “Register” is somewhat ambiguous. In her recent edition, Claire Giordanengo (

Network we obtain from the historian’s expertise.

§14 The vertices and edges of the graph come from the information extracted from the charters only. The colors of the vertices represent the parties to which the corresponding individuals belong. These attributions were made manually. Four parties were defined, by analyzing the way the actors of the network are portrayed in the charters, the

§15 To answer the questions posed in the first section of this article, we have set up a methodology consisting of four blocks. The first one is a procedure for the automatic reconstruction of the parties in the conflict on the basis of a network. This procedure can be used on the network made up of the relations referred to in the diplomatic sources presented above. The second block consists in modifying this basic network by increasing the importance of some of its edges: to do this, we embrace the multi-layer network approach. Third, we compute for each network a metric that quantifies the quality of the parties in conflict that this network allows to reconstruct. Finally, we define a way to account for a hierarchy between certain relationships in the network. The comparisons that we obtain during these steps bring elements of answer to the questions asked.

§16 Before going into those details, we describe the network under consideration in the first subsection. The four other subsections are devoted to the description of the four methodological blocks. All our calculations have been made with the R software (

§17 The 399 vertices of the network we consider in this paper correspond to the protagonists in the conflict presented in Section 2, and people who appear alongside them in diplomatic sources. The 10863 edges of this network, in turn, represent the relationships that these entities maintain in these sources.

§18 These edges have two attributes. The first one is a category, the nature of which represents the type of relationships the two entities maintain in the sources.

Distribution of relations categories within the Cambrai network.

Relation category | Explanation | Number |
---|---|---|

Abbot | X is abbot of Y | 57 |

Alliance | X enters into an alliance with Y | 7 |

Consent | X consents to an action of Y | 31 |

Cosubscription | X and Y both appear among subscribers of some charter | 9457 |

Donation | X gives a property to Y (or confirms such a donation) | 164 |

Kinship | X and Y are parents | 17 |

Notice | X gives notice about an action of Y | 29 |

Request | X requests from Y to take some action | 54 |

Subscription | X appears among the subscribers on Y’s charter | 1047 |

§19 The second attribute of the considered edges is a weight, which is initially defined as the number of charters that attest to such a relationship between the two entities. As we will see, these weights will be modified in order to perform analyses. All the graphs we consider in this paper are therefore weighted.

§20 The first issue we deal with is the automatic reconstruction of the parties in conflict on the basis of a network, no matter how this network was built. Automatic reconstruction of historical political parties has already been undertaken in historiography (see for example

§21 Rather than detecting communities, we identify here the party with which each vertex is associated by using the connections between this vertex and some a priori defined pivot-vertices. It is more a task of graph-partitioning (or graph-coloring) than a task of community-detection. The pivot-vertices are those representing the two candidates for the episcopal see, Walcher and Manasses. The min cut algorithm is a method for partitioning a graph into two subgraphs containing vertices fixed a priori (

Graph partitioning algorithm.

compute d(i, Walcher) ;

compute

The threshold at which a difference in distance is considered to be significant has been set at the 10%-quantile of the series formed by all differences in distance:

threshold = 10% – quantile of {|d(Walcher, j) – d(Manasses, j)| over all vertices j}.

This is the choice that gave the best results (in a sense that will be specified below).

§22 The partitioning method described above is based on the concept of distance between two vertices of a non-oriented weighted graph, which we now need to define. The distance we use is very common (the use of another distance is discussed in Section 4.2). The weight of each edge is first transformed into a cost equal to the inverse of the weight (

§23 To simultaneously process and analyze the interactions of the different categories of relationships in our graph, we embrace the multi-layer network approach. Rather than manipulating a classic network whose edges have an attribute that specifies its category, we consider our network to be the superposition of several sub-networks that we will henceforth call layers (this approach is well know in graph theory literature, see e.g.

§24

Decomposition of an example network into layers corresponding to its edges categories.

§25 In terms of adjacency matrices, the decomposition amounts to a simple sum of matrices: in the case of

§26 Note that, rather than decomposing the left-hand side matrix, this equation allows us to construct a single-layer network from a set of layers. If we know the adjacency matrices of all the layers (i.e. the right-hand side matrices), we can sum them to obtain the adjacency matrix of the multi-layer network resulting from the aggregation of these layers.

§27 It is also possible to apply operations other than the simple sum to aggregate the layers (as it has been done e.g. in

§28 For example, we could aggregate the adjacency matrices corresponding to the four layers of our example network by increasing the importance of the second category using a linear combination with coefficients 1, 3, 1 and 1:

§29 The adjacency matrix resulting from this linear combination (and the network it represents) gives pride of place to the edges of the second category (Subscription). By inflating the coefficient of this type of edges this way, we have made the relationship 3–1 pass in front of the relationship 1–2, and consequently we have modified the network in depth.

§30 To evaluate the relative importance of the different categories of relationships in the Cambrai network, we consider the single-layer networks that result from an aggregation process similar to that of this last example. We use linear combinations in which all layers are associated with a weight of 1, except one, which is associated with a high coefficient (i.e., much greater than 1).

§31 It is then a question of comparing the single-layer networks generated this way, measuring to what extent they correctly reflect the political situation of the conflict. For each of them, we therefore apply the automatic reconstruction procedure presented in Section 3.1. We then compare the parties obtained this way with the parties obtained by the manual partitioning described in

Note that we exclude from this count the vertices that the manual partitioning puts in the “Indeterminate” class.

§32 For each category, we generate not one, but many single-layer networks, gradually increasing the coefficient associated with the category in question. We thus obtain a plot whose x-axis gives the coefficient that has been assigned to the category, and the y-axis gives the classification ratio.

§33 Working with the order in which the witnesses (subscribers) appear in a charter is a different task from that described in the previous section. It is no longer a matter of increasing the relative importance of one category of relationships relative to the others, but of changing the relative importance of relationships that all belong to the same category (the Subscription category).

§34 The idea is as follows. For each charter, we sort the Subscription relationships by the order in which the corresponding individuals appear on the document. We then assign a coefficient to these relationships according to the place they occupy: an item at the top of the list is given a large coefficient, while an item at the bottom of the list is given a small coefficient. The next step in determining the impact of the order of subscribers is to vary the scale of this range of coefficients, from a situation where the relationships are almost on an equal footing (all similar coefficients) to a situation where there is a large difference between the first relationships and the last (very different coefficients).

§35 More precisely, we use the following function: to the

where

§36 As an example, we consider the list of the seven witnesses of a 1108 charter notifying the settlement of a conflict (

List of witnesses of a 1108 charter (

Evolution of the coefficients of ordered witnesses when varying values of parameter

§37 For each value of

§38 In this section, let us first present and comment on the results of the automatic party reconstruction procedure.

Comparison of the parties manually attributed (outer color) and the parties automatically attributed (inner color).

Confusion matrix of the automatic reconstruction of the parties.

automatically attributed parties | ||||
---|---|---|---|---|

Manasses | Walcher | Intermediate | ||

manually attributed parties | Manasses | 159 | 4 | 7 |

Walcher | 18 | 102 | 7 | |

Intermediate | 23 | 8 | 7 | |

§39 Looking at the diagonal of this table yields the general accuracy of the method: for 80% of the vertices whose party is identified by the manual procedure (i.e. whose category is not “Indeterminate”), the two classifications correspond exactly.

§40 In this table most of the vertices that are wrongly assigned by the computer belong to the “Intermediate” party. This is not surprising, since this category is the most uncertain or at least the most difficult to make objective in manual attribution. In a few isolated cases, the sources explicitly mention that some person played a neutral role in the conflict (

§41 Let us now turn to the results of the relative-importance-of-relations assessment.

Evolution of the metric when increasing the importance of each of the nine relationships categories.

§42 A second group of relationship categories consists of Abbot, Donation, and Request, with mid-ranged numbers of attestations. For each of them, one observes a value very close to the dotted line when the coefficient is 0. Not considering these values therefore does not completely destroy the structure of political parties. In addition, values lower than the dotted line are observed when the coefficient is large. Inflating the importance of each of these three types of edges therefore lowers the level of understanding of the conflict.

§43 Note that the low significance of the seven categories analyzed so far does not mean that it is relevant to simply neglect them. The analysis we are conducting considers only the transformations carried out on one of the coefficients of the linear combination at a time (and thus one of the categories at a time).

§44 The case of the Subscription category, which is that of many network relationships, is completely different. The origin of the curve (at the extreme left of the plot) is well below the level of the dotted line: omitting these edges significantly deteriorates the party structure. The curve then rises above the reference value when this category is given greater importance. Links of this type thus have a strong explanatory power within the graph. Understanding of conflict improves when they are considered at a larger extent than those of the Abbot, Donation, and Request categories. Note, however, that the curve stabilizes fairly quickly around a plateau value. This could indicate that, while inflating the importance of these edges improves the metric, it is not necessary to give them an absolutely central place. This could also suggest that the metric is reaching a “maximum” level that the limitations mentioned at the beginning of this section impose on it. These conclusions provide an answer to the first question posed in Section 1 of the paper.

§45 The analysis of the curve of the Cosubscription category makes it possible to take a very clear position on the role of these relations. Omitting them increases the value of the classification ratio, while inflating their importance causes it to plummet. We can thus formulate a rather clear-cut answer to the second question asked in Section 1: it is not relevant to encode cosubscription relations. Historians can therefore spare themselves this long and tedious work, since considering these edges, in addition to making the visual representations of the graph tangled and confused, deteriorates their understanding of the conflict. Note, however, that indirect relations of cosubscription are hidden in the relations of subscription. Indeed, since we consider the edges of the graph to be non-oriented, two vertices A and B, each connected to one of the candidates for the episcopal see, say Manasses, are also connected to each other through it. Even in the absence of cosubscription relations, there is therefore a path between A and B, but it passes through Manasses. Our results show that this indirect path is sufficient to account for the structuring of the network into parties.

§46 Finally,

Evolution of the metric when increasing the parameter alpha (plus a trend curve).

§47 The results presented in the previous section call for technical and historical comments, mainly concerning the working hypotheses used to obtain them. Let us begin with the technical ones, and first discuss the choice of the distance used in the automatic party-attribution procedure. To improve the robustness of our results, we performed all the calculations presented above twice: once with the distance

§48 This counter-intuitiveness is the reason why we have chosen the resistance distance for

Comparison of distances

§49 All of the conclusions presented above were the same when distance

§50 Let us nuance the interpretation of the metric we use to compare graphs. On the one hand, note that in some cases misattribution is inevitable, and does not depend on the design of the partitioning algorithm we have implemented, but rather on the overall approach of our study. This is, for example, the case of the vertex that, in

§51 Let us now turn to historical comments about the method we implemented in this paper. The witness lists must be handled with care in social network analysis. In addition to the methodological difficulties already mentioned in the introduction, to which this article gives some answers, we should bear in mind that some lists are probably incomplete. We could not be sure that the list is complete, as the scribes might have decided to not write the names of all the witnesses present when the action was promulgated (

§52 Another difficulty in the use of the witness lists comes out of the reliability of the charter editions. Most of the Cambresian episcopal charters no longer exist in the original. Some disappeared before the French Revolution, others were destroyed in the bombing of the Belgian State Archives in Mons and Tournai during the Second World War. Consequently, a lot of these documents are only known through cartulary copies and early modern editions. We do not know to what degree these copies are faithful to the original charters. We cannot verify, for instance, whether the author of the copy included all witnesses in his document or whether he read their names correctly. Neither do we know whether he wrote their names in the correct order, as it is sometimes difficult to determine if a witness list is organized horizontally or vertically.

§53 Using a graph to study a historical dossier is a modelling activity. Like any model, the graph gives a simplified representation of the phenomenon it describes. In order to be useful and feasible, the applied simplifications for the analysis should neither be too much nor too little: it is a question of finding the right balance. In this paper, we looked at one aspect of historical network analysis touching on these simplifications. Historians using such tools are often confronted with sets of heterogeneous interpersonal relationships, which have to be brought together to build a network. The method for carrying out this gathering is a working hypothesis, the degree of simplification of which needs to be assessed. This is the analysis we have performed in this article, applied to a network modelling the Cambrai Investiture Contest.

§54 We have seen that the nine categories of edges of this graph are not all equally useful as to understand the structuring of its vertices into parties. Some of them improve the metrics we have constructed to quantify this degree of understanding, others deteriorate it. Simplifications that just neglect the categories of links and consider them all equally should therefore be avoided.

§55 In particular, we have shown that subscription relationships play a prominent role within the graph. Special care must therefore be taken in the collection and encoding of these relations. They cannot be neglected and must be kept in case the graph is reduced (eg., for visualization purposes). Alongside this master category, the other types of relationships, which are generally related to the legal actions of the charters, look pale. Our study associates them with an invisible or slightly negative effect on the degree of understanding of the network structure.

§56 This hierarchy between the categories of edges of the graph also has historical implications that go beyond the methodological aspect, since it runs parallel to a hierarchy between the real-life interpersonal relations of the actors of the Cambrai Investiture Struggle. It shows that these types of relationships are not of equal importance for medieval people, at least in this precise chronological and geographical context. Our results suggest that acting as a witness for an authority was a much more committed action (here, in terms of choosing one side of the conflict) than entering with him into a legal action such as a confirmation, consent or donation. This is, in any case, the representation that medieval people have of it since, again, our methodology is based on a reconciliation of the information given in the charters with that reported in narrative sources.

§57 On the other hand, results about cosubscription relations show a significant negative impact: these edges do damage the picture of party formation we draw from the graph. They can (and should) therefore be omitted, at least when their number is large compared to edges of other types. In doing so, the historian avoids an encoding step that usually entails an important workload and does not risk unbalancing the analyses of the graph.

§58 This result may seem counter-intuitive, when one considers the idea of transitivity of “positive” interpersonal relationships to be natural. Indeed, one might expect that the fact that two individuals are connected to the same third individual would create an interpersonal link of some strength between them. It has been shown in this article that such a direct and full-strength transitivity is not observed for the relations associated with witness lists: integrating into the network cosubscription relations that make the subscription relations transitive does not improve the structure of the automatically retrieved parties. However, we cannot conclude that it is completely absent from our network, since our working hypotheses (considering non-oriented graphs and our choice of distance) imply the existence of an indirect and relatively weak link between two witnesses on the same list.

§59 In the same line of thought, we also answered an issue historians have raised for more than fifty years. We have demonstrated that rank order in the witness lists is not crucial in social network analysis, at least during the high Middle Ages. This result does not mean that the rank of the witnesses in medieval charters was arbitrary. Rank order in witness lists had a social and a political meaning in the Middle Ages, as previous works have demonstrated. However, the rank order is not meaningful in the study of the structure of a network. In such circumstances, even poor editions of medieval charters, in which the order of the witnesses was not respected, may be used in social network analysis.

§60 The results of our study may be useful to historians using witness lists in social network analysis. Nevertheless, they must be confirmed by further inquiries devoted to earlier periods (for instance, the witness lists of the oldest French royal charters studied by

§61 However, even though the result of our inquiry could improve the modelling practices of historians, it makes no doubt that a good understanding of a complex historical phenomenon relies on a quantitative approach as well as on the use of “classical” qualitative methods. These approaches are more complementary than antagonistic. In the case of the Investiture Contest in Cambrai, narrative sources such as the

The authors have no competing interests to declare.

Authorship is alphabetical after the drafting author and principal technical lead. Author contributions, described using the CASRAI CredIT typology, are as follows:

Sébastien de Valeriola: SV

Nicolas Ruffini-Ronzani: NR

Étienne Cuvelier: EC

All authors have contributed equally to this paper. The corresponding author is SV

Conceptualization: SV, NR, EC

Methodology: SV, NR, EC

Software: SV, NR, EC

Formal Analysis: SV, NR, EC

Investigation: SV, NR, EC

Data Curation: SV, NR, EC

Writing – Original Draft Preparation: SV, NR, EC

Writing – SV, NR, EC

Dan O’Donnell, University of Lethbridge, Canada

Els De Paermentier, Ghent University, Belgium

Juri Opitz, Heidelberg University, Germany

Georg Vogeler, University of Graz, Austrian Centre for Digital Humanities and Cultural Heritage, Austria

Shahina Parvin, Journal Incubator, University of Lethbridge, Canada