2014 (with: A. Wanger, S. Kedar, K. Abraham, Y. Cohen, R. Zadok) Quantitative Social Network Analysis (SNA) and the Study of Cuneiform Archives, Akkadika 134: 117-134.

Quantitative Social Network Analysis (SNA) and the Study of Cuneiform Archives : A Test-case based on the Murašû Archive A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok* Abstract : Social network analysis (SNA) is increasingly applied to study archival data, including cuneiform archives, and especially Neo- and Late-Babylonian materials. This paper demonstrates the use of quantitative SNA by means of one example. A network based on 75 documents from the Murašû archive is constructed in order to show a computational, automatic procedure, that demonstrates the potential value of quantitative SNA to cuneiform studies. Keywords : Neo-Babylonian studies, archival studies, social network analysis, network clustering, document classification INTRODUCTION This paper presents a case-study which demonstrates how advanced social network analysis (SNA) can be applied to a cuneiform archive dating to the Late Babylonian period— the (multi-generational) Murašû archive. SNA is common in many fields, yet only recently its utility came to be considered in cuneiform studies. One of the obstacles to successful adoption of SNA methods and perspectives is their reliance on advanced mathematics. The purpose of this paper is to exemplify where quantitative SNA can be useful ; at the same time it aims to be self-contained and accessible to scholars with no training in higher mathematics. Technical and mathematical discussion is therefore limited to the footnotes as much as possible. For the reader’s convenience, technical SNA terms are given in italics when they are first introduced and defined. * This is an extended version of a paper presented by Allon Wagner at the 58th Rencontre Assyriologique Internationale, Leiden, July 18th 2012. This paper is the result of research of the CTIJ (Cuneiform Texts Mentioning Judean and Israelites) group. The research was supported by “Ancient Israel” (New Horizons) Research Program, Tel Aviv University, and by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office. The bulk of this paper was written by Allon Wagner (Tel Aviv University, Ramat-Aviv 69778, Israel, [email protected]) ; Yuval Levavi (University of Vienna, Spitalgasse 2/4, 1090 Wien, Austria, [email protected]) and Sivan Kedar (Tel Aviv University, Ramat-Aviv 69778, Israel, [email protected]) assisted in data collection and interpretation of the results ; assyriological and editorial assistance were provided by Yoram Cohen (Tel Aviv University, Ramat-Aviv 69778, Israel, ycohen1@ post.tau.ac.il) and Ran Zadok (Tel Aviv University, Ramat-Aviv 69778, Israel, [email protected]) and by Kathleen Abraham (University of Leuven, Blijde Inkomststraat 21/3318, 3000 Leuven, Belgium, kathleen. [email protected]). Sincere thanks are extended to Caroline Waerzeggers for sharing her thoughts and unpublished research with us. Bibliographical abbreviations in this paper follow CDLI (http ://cdli.ox.ac.uk/wiki/doku. php ?id=abbreviations_for_assyriology), with the following addition : “Stolper, JCS 53” refers to : Stolper, M., 2001 : « Fifth Century Nippur : Texts of the Murašûs and from their Surroundings », JCS 53, 83–132. Akkadica 134 (2013), pp. 117-134. OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER 117 Akkadica 134 (2013) Network theory is an established scientific discipline at whose foundation lies the understanding that a complex system cannot be fully understood by a reductionist approach, i.e., by studying each participating component in isolation. Rather, network theory shifts the focus of the study by viewing the interactions themselves within the system as components that determine much of its behavior. Network-based analysis has been successfully applied to various fields, such as transportation networks, computer networks and biological networks to name a few.1 One of the thriving sub-disciplines of network theory is social network analysis (SNA), a science that studies the interplay between an individual’s2 attributes (e.g., wealth, authority etc.) and the pattern of interactions this individual keeps with others.3 SNA is a common tool in social sciences, where on the basis of questionnaires and analysis of available datasets social interactions of test-subjects can be reconstructed. There have also been several influential studies that have analyzed historical trajectories on the basis of pertinent primary sources from the perspective of network theory. Padgett and Ansell’s study of the rise of the Medicis to power in 15th century Florence is perhaps best known in this respect (Padgett and Ansell 1993). Their study compellingly demonstrates how the Medicis’ rise to power was mediated by the artful spinning of an intricate network that brought together, through business ties and marriage contracts, families that were not part of the ruling oligarchy. Fig. 1 presents their reconstruction of marriage ties between prominent Florentine families of the era. In the SNA terminology we will shortly introduce, this figure displays a network in which nodes represent families, and edges are drawn according to marriage ties. 1 2 3 BARABÁSI (2002) offers an accessible and non-mathematical introduction to the field. See NEWMAN 2003 ; WATTS 2004 ; NEWMAN, BARABÁSI and WATTS 2006 ; and NEWMAN 2010 for a more thorough treatment. It is quite astounding, as NEWMAN, BARABÁSI and WATTS (2006, 2–3) note, that the same methodology, and the same descriptive language, cast light on manifold phenomena, both man-made and natural. This is one of the most appealing traits of network-based studies. BORNHOLDT and SCHUSTER (2003) present some of the less conventional applications of network-oriented research, such as modeling food-webs, vehicular traffic engineering, and biological networks. For simplicity, we will often refer to the participants in social networks as “individuals” or “persons”. In SNA terminology the participants are rather referred to as actors (or nodes when focusing on network perspectives). Note that actors can represent individuals, but also larger social structures such as families or organizations ; see for instance PADGETT and ANSELL (1993) discussed below. Network nodes do not necessarily represent human entities. In this work, for example, we discuss a network whose nodes are cuneiform texts. Studies of cuneiform societies are likely to benefit from network studies with the nodes being linguistic elements, concepts, or archives. See for instance WAERZEGGERS 2012 for an analysis of a network in which nodes are Neo- and Late-Babylonian cuneiform archives. See the following introductions to social network analysis : WASSERMAN and FAUST 1994 ; DEGENNE and FORSÉ 1999 ; SCOTT 1991 ; PRELL 2011. An historical perspective on the development of the field is offered by SCOTT 1991, 7–38 ; FREEMAN 2004 ; PRELL 2011, 19–50. Many of the developments in SNA were made independently, and predate modern network theory (although not the mathematical branch of graph theory). However, the modern form of SNA (and especially the quantitative aspects stressed in our discussion) relies on mathematics that can be used to describe any network. For this reason our discussion places SNA in the more general context of modern network studies. 118 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network Fig. 1. The network of marriage ties between prominent 15th century Florentine families, according to PADGETT and ANSELL 1993. One family, the Puccis, which had no marriage ties with others, is omitted from the figure. After BORGATTI 2005, 65. It is evident that the Medici family takes a central place in the network. One can even intuitively see that their position is more advantageous than the position of the Strozzis, their rivals. Incidentally, we should mention that the amorphous notion of having an advantageous position in one’s social network is amenable to formal mathematical analysis, and it has been conclusively shown that the Medicis’ position in the network outranks that of the Strozzi family in many aspects.4 Can social network analysis shed new light on cuneiform archives ? This question has been first set forth by Caroline Waerzeggers, who carefully delineated the prospects and limitations of utilizing SNA in Assyriological research.5 Her study also presented, to the best of our knowledge, the first quantitative analysis of a social network reconstructed from cuneiform sources : it demonstrates that the business profile of two Neo-Babylonian individuals is well reflected in the composition of their respective social networks. Waerzeggers concluded her study by stating that despite the challenges which the nature of cuneiform evidence presents,6 “SNA can be an important support tool for Assyriologists ; it will also 4 5 6 See WASSERMAN and FAUST 1994, 169–219 and NEWMAN 2010, 168–193 for a general discussion of quantitative centrality measures, and particularly WASSERMAN and FAUST 1994, 182–183, 192, 197–198 ; NEWMAN 2005, 51–52 ; BORGATTI 2005, 65–69 for the Florentine marriage-network test-case. WAERZEGGERS, forthcoming. The foremost challenges for SNA-based research are incomplete data and difficulties in discerning homonymous individuals (or alternatively identifying persons referred to by two names). See WAERZEGGERS, 15–16. Another aspect of the paucity of data is the lack of panoramic primary sources that give an overview of the entire social fabric in a given time period, e.g. marriage lists. In Assyriology, we are mostly limited to data revolving around one institution, family etc. Consequently, cuneiform data lends itself more easily to ego-centered analyses (WAERZEGGERS, 8, 16). And see PRELL 2011, 118–133 for an introduction to ego-centered networks. 119 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) help to tackle research questions that cannot be answered with standard methods.” In order for SNA to be advantageous, she adds, we do not have to utilize its entire mathematical apparatus, which assumes availability of data that cuneiform sources often do not have ; SNA can be used to direct research, its perspective and terminology forming a convenient way to ask novel questions and formulate answers concerning ancient societies. Taking Waerzeggers’ conclusion as our departure point, we wish to demonstrate the potential of approaching data gleaned from cuneiform archives from a quantitative SNA perspective. BUILDING BLOCKS OF A NETWORK7 Let us introduce some key SNA terms crucial for understanding the operational procedures used later.8 The fundamental concept of network theory is the graph.9 A graph is a collection of nodes representing, for instance, persons, and edges which encode relationships (ties) between each two nodes. We have already seen in Fig. 1 the common representation of a network, in which nodes are marked as circles and edges as lines connecting them. In a social network, an edge between nodes A and B can represent any kind of relationship between them : A is a neighbor of B, A is the father of B, A gave a loan to B, etc. We note that the first relation is symmetric (if A is a neighbor of B, then B is a neighbor of A) and in this case we say that the corresponding edge is undirected. The other two relationships (where A is the father of B, or A gave a loan to B) are asymmetric, and hence the corresponding edges are directed. Graphically, directed edges are represented as lines with an arrow head going, for instance, from father to son, thus indicating which node is the father of which. For undirected edges there is naturally no need to denote a direction to the relationship (Fig. 2). Edges can also be weighted (or valued) meaning that they are associated with a certain quantity. For instance, the directed tie “A gave a loan to B” might be accompanied by the sum of the loan. These weights could be useful, for instance, to discern the more important business transactions that took place in the network. Fig. 2. Examples of possible tie-types. 7 8 9 See nn. 1 and 3 for relevant references to this section. We slightly elaborate beyond what is strictly required for the current paper (e.g., in the discussion of directed vs. undirected ties) for the sake of completeness of the introduction to a reader unfamiliar with SNA. While the terminology and methodology on which SNA is based borrows heavily from graph theory, the latter field is distinctly different from network studies such as discussed here. See NEWMAN, BARABÁSI, and WATTS 2006, 4–6. 120 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network The concepts described so far are quite intuitive, and, no doubt, many scholars have described such relations in words, perhaps at times with the help of diagrams such as the ones presented in Fig. 1., without any awareness of SNA terminology and its applications. Yet here we reach the fundamental obstacle to a successful application of SNA. When a social network spans dozens or even hundreds of individuals, the pattern of interactions becomes too complex to be manually traced.10 For example, each of the two Late-Babylonian networks that Waerzeggers studied contain hundreds of individuals, which makes it difficult to grasp the underlying social structures or dynamics of these networks. In order to tackle this challenge, SNA has developed over the past decades an impressive arsenal of unique mathematical methods. TWO-MODE NETWORKS All networks we have discussed so far were one-mode networks : these are networks in which all nodes represent the same social entity, such as an individual, a family, or an archive. Sometimes, however, it is useful to consider two-mode networks in which nodes represent two different entities. In other words, the nodes are divided into two non-overlapping sets (modes). A particularly common type of two-mode networks is affiliation networks, which relate a set of actors (the first mode) to some social activity (the second mode).11 A hallmark example for an affiliation network is the study of Davis et al. that collected data on 18 rural Mississippi women, who had participated in a series of 14 social events over the course of 9 months.12 Not all the women took part in all of the events, and so the researchers generated a network13 with two categories of nodes : an individual and a social gathering, and traced which women participated in each gathering. Part of their data is shown in Fig. 3 : triangles represent women, circles the social events. A tie indicates that a certain woman participated in a certain social gathering, and so ties are drawn only between the two sets.14 Davis et al. used their data to investigate the extent by which one’s social class effects one’s daily social life. 10 11 12 13 14 In her survey of SNA literature from an Assyriologist’s perspective, Waerzeggers commented : “I get the impression that most studies limit the number of actors under observation so as to make the data set more manageable. I.e. Padgett and Ansell look at important Florentine families, not at individuals. In this way, a dataset of tens of thousands of people is reduced to 92 ‘actors’” (WAERZEGGERS, forthcoming, note 24 ; emphasis is Waerzeggers’). WASSERMAN and FAUST 1994, 291–343. DAVIS, GARDNER and GARDNER 1941, chap. 7, and see especially pp. 147ff. and Fig. 3 which shows a twomode network in matrix form. The data concerning participation of 18 women in 14 social events is actually only a small subset of their data, chosen for illustrative purposes. However, this small subset had substantial impact on SNA and was commonly used to motivate and exemplify further network-flavored analysis, see HOMANS 1951, 82–84 ; BREIGER 1974 ; BREIGER, BOORMAN, and A RABIE 1975, 356–358 ; DOREIAN 1979 ; DOREIAN 1982 ; DOREIAN 1986. As this study was published in 1941 the authors were not aware of network terminology and did not present their data, nor their method, in such a way. We use network-terms, however, to describe their work in order to highlight its relevance to the sociologically-motivated network analysis. In graph theory, a graph in which the nodes can be divided into two non-overlapping sets, and edges are formed only between these two sets is called a bipartite graph. 121 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) Fig. 3. An example of an affiliation network. The network shown is a subset of the data collected by Davis et al. 1941, chap. 7. The ties show which women (triangles) participated in which social events (circles). Two-mode networks are particularly apt in Assyriology, where one can build networks associating persons to the texts that mention them. The two types of nodes are thus individuals and texts. These networks offer two appealing traits : first, they are easily gleaned from the data. When a digital version of the tablets is available, for instance through the ORACC15 or Archibab16 initiatives, the process can be even automated to a large extent. Second, they can be easily transformed back into a one-mode network, the main object of SNA study, via routine mathematical manipulation.17 Admittedly, the simplicity of the procedure does not come without cost. Networks which are reconstructed this way carry less data than straightforward and laborious reconstructions of one-mode networks. For example, they do not differentiate between the different roles of individuals in the texts, such as buyer vs. seller. However, these networks still offer valuable insights. In this study, we took a middle-ground : on the one hand, we rely on an easily-generated affiliation-network. On the other hand, this network was manually curated, and so it was possible to slightly refine the data as described below. AUTOMATIC CLASSIFICATION OF TEXTS FROM PHASES BASED ON A TWO-MODE NETWORK THE MURAŠÛ ARCHIVE INTO CHRONOLOGICAL Classification of archival documents into subgroups, such as separate chronological phases within the archive, is an intricate process, because it involves the collection and the assessment of diverse types of evidence. This process becomes inevitably formidable when dealing with very large archives. Similar problems encountered in many fields of science are 15 16 17 Open Richly Annotated Cuneiform Corpus, http ://oracc.org http ://www.archibab.fr WASSERMAN and FAUST 1994, 307–312 ; NEWMAN 2010, 123–126. 122 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network nowadays approached with automated tools based on the discipline of machine learning.18 Here, we focus on the task of unsupervised clustering : the computer is given a set of objects and then it classifies them into groups (clusters), such that the objects in each group are in some sense similar to one another.19 In our case-study the objects are archival documents. Our purpose is to classify the documents into meaningful groups on the basis of network data.20 We will show that our classification scheme successfully divides 75 texts of the Murašû archive into two chronological phases. When discussing automated classification it is important to keep two points in mind. First, the classification suggested by the computer is by no means perfect or complete. It is better to treat the computer-suggested classification as a working hypothesis, rather than as a conclusive result. Second, when proposing a classification scheme (such as the one we propose below), one must offer some objective validation. Simply listing the resulting clusters and finding some coherence in each of them is not enough because such a process is completely subjective. The value of a classification scheme can only be measured against a priori known data that were not used in the process of the clustering itself. For that reason, we purposefully selected many dated texts for our analysis. However we did not make the dates available to the computer. Nonetheless, the resulting subgroups adhere almost completely to two distinct chronological phases, thus validating our method in an objective manner. We have constructed a two-mode network of 883 individuals mentioned in 75 representative documents of the Murašû archive (listed in appendix A).21 A part of the network is shown in Fig. 4.22 The triangles represent individuals and the circles texts. Edges are drawn between persons and the texts which mention them. In order to simplify the network construction process, we do not differentiate between the various roles a person can take in a documented business transaction, although such distinctions can be made in future studies. However, since the network was manually constructed (unlike automated construction, see above), we can refine the data as follows : we exclude from the analysis links between persons and texts, where the former were mentioned as the father, or other ancestor, of one of the parties. Links of this type are obviously less informative because the ancestor is not taking part in the documented transaction. However, the information that can be learned from links 18 19 20 21 22 MITCHELL 1997. See JAIN and DUBES 1988 ; EVERITT et al. 2011. Note that the Girvan-Newman algorithm, which we employ, is not generally considered a method of unsupervised clustering because it is geared towards finding communities in a network (see below and n. 26). This is a related but not an identical concept to clusters. Here, however, we ultimately employ the algorithm to generate clusters of texts by a chronological division, which is a task of unsupervised clustering. Clearly, our sample (less than 10% of the texts in the archive) includes merely a small fraction of the prosopograpy of the Murašû archive, which consists of thousands of individuals. The current contrubtion seeks to present a new method to analyze cuneiform data rather than to offer an exhaustive study of this particular archive. We restrict ourselves to a subset of the network only for visualization purposes, since the full network is too large to be visualized conveniently. 123 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) between persons and texts, where the person serves as a witness to a documented business transaction, is more ambiguous. While there are clear cases of witnesses who were regular participants in the Murašû’s business activity,23 most of the witnesses are mentioned in only one text. It is possible that some of them were present at the occasion of concluding the transaction by pure coincidence, and had nothing to do with the case in hand.24 For these reasons, we link a person to a text in which he appears as a witness only when that person is mentioned in another place in the document, apart from the witness list, or when his seal is impressed to the tablet. A person whose seal is impressed to the tablet was always considered one of the participants in the transaction. In summary, our reconstructed affiliation-network does not simply associate persons with the texts in which they appear. It associates persons with documented business transactions in which they took part : a person is linked to a text only if he actively participated in the business transaction documented therein. This two-mode network can be transformed into a person-to-person one-mode network, and studied in a similar way to the networks we have presented so far. Here, however, we transform it into a one-mode text-to-text network.25 For the purpose of explanation, Fig. 5 presents the text-to-text network that would have been obtained had we limited ourselves to studying only the partial data shown in Fig. 4. Fig. 4. A subset of the two-mode person-to-text network we have constructed for the Murašû archive. Fig. 5. The results of an algebraic procedure that transforms the sub-network shown in Fig. 4 into a valued text-to-text network. 23 24 25 Two striking examples are Aqar-aplu/Iddinâ, who appears in our data set in 19 texts (in 15 as a witness), and ErƯba-Illil/Illil-bana who appears in 17 texts (in 13 as a witness). Aqar-aplu, son of Iddinâ, occurs in over 160 documents of the Murašû archive and ErƯba-Illil, son of Illil-bana, in no less than 140, mostly as a witness. For their function as witnesses, cf. CUSSINI 2013, 46. The phenomenon of recurrent witnesses in this archive has already been noticed by CARDSACIA 1951, 20. For the use of coincidentally-chosen versus deliberately-selected witnesses, see VON DASSOW 1999, 5–7. See n. 17 above. The transformation from two-mode network to one-mode network is algebraic and requires no additional data processing on the part of the researcher. 124 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network In this text-to-text network, each node represents one of the 75 texts. An edge is drawn between texts that mention the same individual (more precisely, the individual actively participating in the transactions documented in both texts, see above). Note that this edge is weighted by the number of such individuals. For instance, according to Fig. 4 (based on a subset of our data) there are two persons mentioned both in BE 10 5 and in BE 9 59 – these are Illil-šuma-iddina/Murašû and Illil-šuma-iddina/Tattannu. Therefore, in Fig. 5 (which is based only on the subset of data in Fig. 4) the edge between these texts has a weight of two. All the other pairs of texts share only one person among them in Fig. 4, and therefore their respective edges have a weight of 1. One may wonder what is the purpose of building a two-mode network and then transforming it into a one-mode text-to-text network, in place of building the one-mode text-totext network directly. To answer that, we must remember that manually constructing a onemode text-to-text network is excruciatingly laborious. For instance, in order to accommodate our 75 representative texts we should have considered 2775 pairs of texts, and examine when does a pair of texts make reference to the same individuals. Building the two-mode network, on the other hand, is quite simple, and its transformation to text-to-text network is a matter of pure algebra carried out automatically. The network described in this study was built in several hours of manual work. In order to see how this network can be used to divide the group of texts into meaningful subgroups, we shall now define the notion of a community within a network. Communities are groups of nodes that are tightly connected among themselves, but only loosely connected to others (Fig. 6).26 Since in our network an edge between two texts denotes that both mention the same individual as an active participant, it follows that communities in that network are groups of texts that mention similar sets of individuals (as active participants) while making less frequent references to others. We expected such groups of texts to form distinct units within the archive. Fig 6a. A model network with three communities : three densely connected groups of nodes, which are only sparsely connected among themselves. Wide lines and thin lines are ties that connect two nodes in the same community, or two nodes that belong to two different communities, respectively. After GIRVAN and NEWMAN 2002, 7822. 26 A precise definition and a review of methods for finding community structures in networks can be found in NEWMAN 2004a ; NEWMAN 2010, 371–391, but see on the other hand LESKOVEC et al. 2008 ; LESKOVEC, LANG, and M AHONEY 2010. See also XIE, K ELLEY, and SZYMANSKI 2013 for a review of methods that are capable of detecting overlapping communities. The term “community” is usually used in the complex-networks literatures, while sociological studies prefer the term “cohesive subgroup” (WASSERMAN and FAUST 1994, 249–290 ; PRELL 2011, 151–165). Cohesiveness is a more general concept, however, and encompasses several SNA approaches. The most pertinent approaches, for the purpose of the current study, are ones that emphasize that in order for a subgroup to be cohesive it need not only have relatively strong ties among its members, but also relatively weak ties to the outside. See WASSERMAN and FAUST 1994, 267 and the references therein. 125 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) Fig. 6b : A social network of scientific collaboration within a private research institution. Nodes are scientists, and ties are drawn between scientists who co-authored at least one paper. After NEWMAN 2004b, 5201, who notes : “This particular network appears to divide into a number of subcommunities, as indicated by the shapes of the nodes, and these subcommunities correspond roughly to topics of research” (also indicated in the figure). The Girvan-Newman algorithm27 is a computational method for detecting community structures in networks. Here, we applied it in order to divide a group of texts within the Murašû archive into sub-categories. We supplied a computer program with a list of texts and the people appearing in them (equivalent to the person-to-text network described above). The progam transformed it into a text-to-text network,28 and applied the Girvan-Newman algorithm to that network. The output of the program is thus a proposition as to how to divide the texts in our dataset into sub-groups. We stress that no other information was available to the program, such as chronological information, the number of sub-categories we expect to find in the data etc. All of its computations are based on the associations of people with texts. Having been supplied with this data, the algorithm proposed the classification29 shown in Fig. 7 ; Fig. 8 is a reproduction of Fig. 7, which highlights several texts of particular interest that are discussed below. 27 28 29 GIRVAN and NEWMAN 2002. A full description of the algorithm is mathematically-involved and beyond the scope of the current work. For an evaluation of the Girvan-Newman algorithm compared with possible alternatives, see the references in n. 26 above. The Girvan-Newman algorithm does not use the weights on the edges of this network. We included them in our description of the network for completeness’ sake, and since they hold valuable information on the strength of ties in the network, which can be used in future work. For a proposed generalization of the Girvan-Newman algorithm to weighted networks see NEWMAN 2004c. In fact, the Girvan-Newman algorithm does not produce a unique community structure of the network but rather a hierarchy of communities, representing different levels of granularity. I.e., the hierarchy represents a division into communities, and then a further division of these into smaller communities, and so on. For the 126 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network Fig. 7. The clusters generated by running the Girvan-Newman algorithm on the Murašû archive network we have assembled (choosing a granularity as detailed in n. 29). Fig. 8. A reproduction of Fig. 7 highlighting several nodes of special interest that are discussed in the main text. purpose of the current work, we selected the division which had the highest quality. In mathematical terms, we chose the granularity whose community structure had the highest modularity. Modularity – often denoted Q, for instance by the UCINET (BORGATTI, EVERETT and FREEMAN 2002) and NetDraw (BORGATTI 2002) software – quantifies the quality of the partition of the network into communities. More accurately, it quantifies how well does an assumed partition adhere to the rule that communities should have many links among their members, but sparser links to the outside world. The suggested partition into communities of the network discussed in this paper achieves modularity Q = 0.319. No other significantly-different partition of the same network achieves a comparable modularity. The precise defi nition of modularity is mathematically-involved and beyond the scope of this paper ; see NEWMAN and GIRVAN 2004 ; NEWMAN 2004a, 326–327 ; NEWMAN 2010, 223–226. A list of further community-quality measures is given by LESKOVEC, LANG, and M AHONEY 2010, 636–638. 127 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) The resulting classification closely follows two chronological phases within the archive : an earlier phase (blue group, on the left) in which Illil-šuma-iddina/Murašû was the main protagonist, and a later phase (red group on the right) in which his nephew, RƝmnjt-Ninurta// Murašû, assumed that role. One can verify the validity of the classification by inspecting the dates of tablets within each group : clearly, the blue group mostly belongs to the late years of Artaxerxes I (465–424/3), while the red group mostly belongs to the early years of Darius II (424/3–405). We emphasize again that the dates were not used in the process of classification, but rather used only in posterior validation of its accuracy. This proves the validity of our classification method in an objective manner. Once proven valid, our results can bear on the dating of undated texts and on the identification of ambiguously-named persons within them (e.g., people whose names are broken). For example, we can see that the undated texts number 67 and 68 (in the top left, see also Fig. 8) were classified with the blue group, whereas texts 69 and 72 (lower right corner, see also Fig. 8), whose dates are broken or incomplete, were classified as red. We have thus obtained a working hypothesis concerning a chronological division within the archive, and the possible place of undated texts along this division. The main strength of algorithmic, network-based classification is its ability to take into account indirect associations that are not easily seen by a scholar studying the relevant corpus. An example for this is offered by text no. 51 in our dataset (PBS 2/1 185), dated 1 Dar II. This text was correctly classified by the Girvan-Newman algorithm as belonging to RƝmnjt-Ninurta’s phase, although RƝmnjt-Ninurta does not appear in it.30 However, other actors in that text enabled to classify it correctly. Text 51 concerns actors such as the scribe Ninurtaaba-uৢur/Illil-šuma-iddina, who worked for RƝmnjt-Ninurta at other occasions. In fact, he authored 24 texts in our datasets on behalf of RƝmnjt-Ninurta, of which two were written in 40 Art, and the others are subsequent to Darius II’s accession. Hence, texts in which this scribe figures are clearly associated with the later chronological phase in the archive. A late date for Text 51 is also clear from the participation of Murašû, son of Illil-suma-iddina, in the transaction. He appears in three other documents from the archive (not part of our dataset), dated between 424–416 BCE (STOLPER 1985, 20 n. 77), and hence he is roughly contemporary with RƝmnjt-Ninurta (attested between 429–415/414 BCE). Another illuminating example is provided by text no. 75 (UCP 9/3), which mentions both Illil-šuma-iddina and RƝmnjt-Ninurta. The appearance of both actors conforms to its date, 2 Dar II, which lies in the transition between the two chronological phases. The algorithm placed it in the later chronological phase (red group), in which RƝmnjt-Ninurta is the main protagonist. Although both RƝmnjt-Ninurta and Illil-šuma-iddina are associated with this transaction (as opposed to witnesses, or ancestors of the actors, who are excluded, as discussed above), a closer examination of the text shows that it is indeed RƝmnjt-Ninurta who is the leading actor in this case. According to this document, RƝmnjt-Ninurta provides a certain GadalyƗma with a horse, equipment and provisions for the purpose of royal service (‫܈‬ebnjtu 30 The text has Murašû/Illil-šuma-iddin//Murašû among the main actors. As far as our algorithm is concerned this does not count as an appearance of Illil-šuma-iddin in the text, because it ignores father names. 128 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network ša šarri, l. 11) in Uruk. The royal service is due for the share of the Murašû family in a horse fief (bƯt sƯsî), and GadalyƗma is being sent as replacement for the Murašûs. Illil-šuma-iddina, on the other hand, is mentioned only as the one who had inherited the share in the horse fief (l. 5), in reference to a past event. As in the case of PBS 2/1 185 mentioned above, the correct assignment of text no. 75 (UCP 9/3) to the late group of RƝmnjt-Ninurta is probably due to the identification by the computer of its author, the scribe Ninurta-aba-uৢur/Illil-šuma-iddina, and two other individuals associated with the business activity of RƝmnjt-Ninurta, ArdƯya/Bullu৬â and Illil-kƝšir/ Arad-Illil. They witnessed the transaction that is recorded in text no. 75 and their seals are impressed on the tablet. The seals of both men are found on six additional texts from RƝmnjtNinurta’s dossier that are in our dataset.31 Incidentally, we have also learned that the algorithm can correctly classify a text that belongs to the Illil-šuma-iddina phase even when both Illil-šuma-iddina and RƝmnjt-Ninurta appear in it due to an error on our part. Early on our research, we introduced an inadvertent error into the dataset by marking that RƝmnjt-Ninurta appears in text no. 62 (EE 86), although only Illil-šuma-iddina is actually mentioned in it. Unaware of our error, and assuming that RƝmnjt-Ninurta is the dominant actor in the text, we were surprised to learn that the Girvan-Newman algorithm associated this text with the earlier chronological phase. A closer inspection revealed the error.32 Even before the error was rectified, however, the correct classification of this text is illuminating. Even though RƝmnjt-Ninurta was (incorrectly) marked as appearing in the text, the text was clearly embedded in the network of texts belonging to the earlier chronological phase, and this is what enabled its correct classification. Text no. 62, whose date is largely broken ([x] Art), records a barley debt owed to Tirikammu, a subordinate (mƗr bƯti) of Illil-šuma-iddina. Tirikammu appears once more in our dataset as a subordinate of Illil-šuma-iddina, in text no. 65 (EE 94) again from 37 Art, which firmly situates him in the early phase of the archive.33 An additional connection between text no. 62 and the early group of Illil-šuma-iddina texts is Iaপnj-natanna/Iadiপyama, the debtor, who is also mentioned in texts nos. 2 (BE 9, 25, dated 31 Art, as a witness only) and 64 (EE 92, 40 Art), both associated with the dossier of Illil-šuma-iddina. Several texts were not classified within either of the two main phases. Text no. 27 (JCS 53, pp. 86-87, no. 1), for example, is set aside and connected to the blue group only by one tie. This text is much earlier than all others in our sample (dated 18 Art), yet it is strongly connected to Text 28 (JCS 53, 2) because they have two common participants (঩annƯya/ Iddina-BƝl and Arad-Illil/Iddinâ). It is interesting to note that a third participant in this transaction is Murašû himself, who is mentioned in other texts in our sample only as a father or 31 32 33 ArdƯya/Bullu৬â : BE 10, 83 ; PBS 2/1, 107 ; Illil-kƝšir/Arad-Illil : BE 10, 94 ; PBS 2/1, 74, 89, 203. For more tablets from the Murašû archive that bear ArdƯya’s or Illil-kƝšir’s seal, see BREGSTEIN 1993, nos. 535 and 247. We repeated all computations described in this paper following the correction of the error. All the results presented, save for the one described in this paragraph, were obtained following the correction. Tirikammu is further attested in another 10 texts of the Murašû archive (ZADOK 2009, 302–303 : 525). The dated ones span from 37 Art to 1 Dar and whenever his master is mentioned (in seven documents) it is Illil-šumaiddina, so that there is little doubt that undated texts that mention him belong to the early phase of the archive. 129 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) an ancestor. All things considered, this text seems to belong to an even earlier phase than the one that revolves around the activity of Illil-šuma-iddina/Murašû. Thus its classification separately from any of the two main phases is well-grounded. Another texts which was listed as not belonging to any of the phases is text no. 74 (JCS 53, pp. 96-99, no. 7). This text is particularly noteworthy since it is, in fact, not a part of the Murašû archive but rather belongs to the šaknu of Nippur (STOLPER 2001). Nevertheless, it has connections with seven other texts in our sample, mainly in the red group, thanks to its participants Iddina-Marduk/Uballissu-Marduk, Ninurta-ana-bƯtišu/Lnj-idƯya and Illil-šumalilbir/NƗdinu, who participated in other transactions as well.34 Although the connections are numerous, the text is not embedded in any of the two phases. This led the algorithm to exclude it from both phases without any prior knowledge that this text does not belong to the Murašû archive. This demonstrates that the algorithm is not only able to leverage indirect ties to associate texts with one of the phases even when there are no apparent connections between them, as we have seen so far ; it can also disassociate a text from a phase, when there are seemingly strong ties between them, that in fact are not as strong as they may seem in a cursory inspection of the data. CONCLUSIONS This study presented one test-case in which quantitative SNA analysis was applied to cuneiform archival data. We reconstructed an affiliation network based on a subset of the Murašû archive, and used it to perform an automatic classification of the texts into two chronological phases. Such an observation is not trivial to come by for a scholar studying that material, and even more so when the number of pertinent texts increases to many hundreds. The importance of this study is two-fold. First, it demonstrates the utility of adopting SNA methodology to the study of cuneiform societies, a trend that seems to strengthen now with the publication of further works that adopt an SNA approach.35 We agree with Waerzeggers that SNA terminology is useful in itself and that one can benefit from it even without adopting complex mathematical means ;36 an SNA perspective allows raising questions and formulating answers that otherwise can not be easily approached.37 Secondly, this study demonstrates the benefits of employing quantitative and computational approaches where large volumes of data are concerned. Computer algorithms are capable of discerning subtle patterns in the data that are not easily seen by a scholar overwhelmed with dozens and hundreds of texts and numerous factual details. We expect that the ongoing progress in the creation of large-scale online 34 35 36 37 Idinna-Marduk/Uballissu-Marduk : IMT 84 and EE 107 ; Illil-šuma-lilbir/NƗdinu : BE 10, 92, PBS 2/1, 107, PBS 2/1, 203 and EE 34 ; Ninurta-ana-bƯtišu/Lnj-idƯya : BE 10, 60, PBS 2/1, 50 and PBS 2/1, 148. This was noticed by STOLPER 2001 : 98-99. See WAERZEGGERS 2012 and STILL 2012. Some of the standard SNA analyses are unsuitable for cuneiform archives and have to be adapted seeing the unique challenges cuneiform evidence presents. See n. 6 above. WAERZEGGERS forthcoming, 16. 130 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network repositories of cuneiform data38 will result in an increasing need for such methods, rendering them particularly advantageous. APPENDIX A No. Text 1 BE 9 3 13 Art 2 BE 9 25 31 Art 3 BE 9 28 31 Art 4 BE 9 34 5 BE 9 45 6 BE 9 59 P261607 37 Art 7 BE 9 69 P261612 39 Art 8 BE 9 86a P261499 41 Art 9 BE 10 5 0 Dar II 10 BE 10 7 0 Dar II 11 BE 10 39 P261555 1 Dar II 12 BE 10 60 P261557 2 Dar II 13 BE 10 65 P261555 3 Dar II 14 BE 10 76 P261400 3 Dar II 15 BE 10 77 P261188 3 Dar II 16 BE 10 83 P261553 4 Dar II 17 BE 10 84 P261460 4 Dar II 18 BE 10 85 P261561 4 Dar II 19 BE 10 92 P261335 4 Dar II 20 BE 10 94 P261475 4 Dar II 21 BE 10 118 P261519 7 Dar II 22 BE 10 128 P261470 7 Dar II 23 IMT 7 (Ni 501) 34 Art 24 IMT 84 (Ni 2845+PBS 2/1 64) 3 Dar II 25 IMT 94 (Ni 519) 40 Art 26 IMT 95 (Ni 550) 4 Dar II 27 Stolper, JCS 53, 1 (NBC 6148) P293067 18 Art 28 Stolper, JCS 53, 2 (NBC 6206) P293122 29 Art 29 PBS 2/1 5 P263898 1 Dar II 30 PBS 2/1 12 P267433 1 Dar II 31 PBS 2/1 27 P261368 1 Dar II 38 CDLI No. P261590 Date 34 Art 36 Art Such as ORACC (Open Richly Annotated Cuneiform Corpus, http ://oracc.org) and Archibab (http ://www.archibab.fr) mentioned above. 131 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER Akkadica 134 (2013) No. Text CDLI No. Date 32 PBS 2/1 32 P261384 1 Dar II 33 PBS 2/1 50 P261678 3 Dar II 34 PBS 2/1 53 P261640 2 Dar II 35 PBS 2/1 60 36 PBS 2/1 63 P263897 3 Dar II 37 PBS 2/1 72 P267459 3 Dar II 38 PBS 2/1 74 P267488 3 Dar II 39 PBS 2/1 76 P267454 3 Dar II 40 PBS 2/1 84 P267437 4 Dar II 41 PBS 2/1 85 42 PBS 2/1 89 P263895 4 Dar II 43 PBS 2/1 104 P267470 5 Dar II 44 PBS 2/1 107 P263893 5( !) Dar II 45 PBS 2/1 108 P261517 5 Dar II 46 PBS 2/1 115 P261436 5 Dar II 47 PBS 2/1 119 P267491 6 Dar II 48 PBS 2/1 121 P267468 6 Dar II 49 PBS 2/1 133 P267429 7 Dar II 50 PBS 2/1 148 P267471 11 Dar II 51 PBS 2/1 185 1 Dar II 52 PBS 2/1 203 4 Dar II 53 PBS 2/1 205 4 Dar II 54 PBS 2/1 208 5 Dar II 55 PBS 2/1 222 7 Dar II 56 EE 2 (CBS 04993 + CBS 13050) 57 58 59 EE 34 (BM 12957) 60 EE 35 (CBS 5240) 61 62 3 Dar II 4 Dar II P261186 [24] Art EE 16 (CBS 05186) P261378 34 Art EE 24 (CBS 12986) P267590 [x] Art 7 Dar II P261433 33 Art EE 65 (CBS 04987) P261180 41 Art EE 86 (CBS 12924) P267526 [x] Art 63 EE 91 (CBS 05213) P261406 5 Dar II 64 EE 92 (CBS 05510) P261703 40 Art 65 EE 94 (BM 13264) 66 EE 98 (CBS 5170) P261362 37 Art 36 Art 67 EE 100 (CBS 5212) P261405 ? 68 EE 107 (CBS 12829) P267430 ? 69 EE 111 (CBS 12985) P267589 [7 Dar II] 70 EE 113 (CBS 13089_ P268174 33+ Art 71 Stolper, JCS 53, 3 (NBC 6122) P293043 31 Art 72 Stolper, JCS 53, 5 (L-29-554) 6 [Dar II] 132 OFFPRINT AKKADICA 134 (2013), fasc. 2 - COPYRIGHT CENTRE ASSYRIOLOGIQUE GEORGES DOSSIN THIS DOCUMENT MAY BE PRINTED FOR PRIVATE USE ONLY. THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER A. Wagner, Y. Levavi, S. Kedar, K. Abraham, Y. Cohen, R. Zadok, Quantitative Social Network No. Text CDLI No. 73 Stolper, JCS 53, 6 (CBS 5316) P261510 74 Stolper, JCS 53, 7 (YBC 11564) 75 UCP 9/3 275-277, pl. 1 Date 31 Art 4 Dar II P247869 2 Dar II BIBLIOGRAPHY BARABÁSI, A.-L., 2002 : Linked : The New Science of Networks, Cambridge. BORGATTI, S. P., 2002 : NetDraw Software for Network Visualization, Lexington. BORGATTI, S. P., 2005 : « Centrality and network flow », Social Networks 27 (1), 55–71. BORGATTI, S. P., EVERETT, M.G., FREEMAN, L. C., 2002 : Ucinet for Windows : Software for Social Network Analysis, Harvard. BORNHOLDT, S., SCHUSTER, H. G. (Eds.), 2003 : Handbook of Graphs and Networks : from the Genome to the Internet, Weinheim. BREIGER, R. L., 1974 : « The Duality of Persons and Groups », Social Forces 53 (2), 181–190. BREGSTEIN, L. 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THIS DOCUMENT MAY NOT BE DISTRIBUTED, STORED IN A RETRIEVAL SYSTEM WITHOUT PERMISSION OF THE PUBLISHER