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Dyads and Triads in Community Detection: a view from the Italian Bronze Age

Emma Blake
p. 28-32


Alors qu’en archéologie l’utilisation des analyses de réseaux sociaux gagne en maturité, de nouvelles approches peuvent être intégrées à l’outillage de la discipline. L’étude des structures locales, de la relation des nodes et des nœuds au sein des réseaux, en particulier dyadiques et triadiques, est considérée depuis longtemps comme un domaine important pour les analyses de réseaux sociaux. Toutefois, ce domaine est resté virtuellement ignoré des archéologues. Faute de données abondantes, ils ont surtout axé leurs études de réseaux entiers sur une échelle macro, ou bien sur celle du rôle de nœuds spécifiques dans des réseaux. Des études à échelle micro permettent d’aborder les propriétés structurelles du réseau et peuvent servir à comparer des caractéristiques de réseaux qui ne seraient pas perceptibles à partir de mesures de densités ou d’autres mesures de connectivité à macro-échelle. Cet article aborde les concepts de triade et de transitivité et les met en œuvre avec une étude de cas: les réseaux de sites archéologiques liés par la présence de types d’artefacts particuliers dans la péninsule italienne à la fin de l’âge de Bronze. Il démontre que des études à micro-échelle de ce type peuvent apporter des informations nouvelles sur la structure des réseaux archéologiques.

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Entrées d’index

Index de mots-clés :

dyade, nodes, transitivité

Index by keyword:

Bronze age, dyad, Ilaty, nodes, transitivity

Index géographique :


Index chronologique :

âge du Bronze
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Texte intégral


1As archaeological applications of social network analyses mature, new approaches may be incorporated into the network analysis ‘toolkit’ for archaeologists. One potential area for analysis that has long been important in social network studies but to date has been virtually ignored by archaeologists is the study of local structure, the relations of nodes and ties within networks, particularly dyads and triads. With relatively sparse datasets most archaeologists have focused on macrolevel studies of entire networks, or else the roles of particular nodes in networks (for the former, see for example Ruffini 2008; for the latter, see Mizoguchi 2009). In part this has suited archaeologists’ research questions, as studies of network connectivity and centrality are not illuminated through analyses of lower order structures. However, microlevel studies offer insights into the structural properties of a network and may provide bases for comparisons of network characters that would not be apparent from density measures or other macrolevel measures of connectivity alone. This paper examines the triad census and the related concept of transitivity, applying them in an exploratory manner to an archaeological dataset to see what, if anything, these local structure analyses may offer to our interpretations.

Final Bronze Age regional networks in Italy

2The case study employed here are the six regional social networks present in peninsular Italy in the Final Bronze Age, 1200-950 BCE. In an earlier study I detected these networks from the co-presence of particular exotica and other highly traceable goods at contemporary sites (Blake 2013, 2014). I treated the find spots as nodes, and configured the relations such that those nodes with the same object type present, and no more than 50 km apart, had a tie. The premise behind this network design is that in the small scale and hyper-localized societies of Bronze Age Italy, objects, once they reached an area, would have circulated locally. Overland travel was dangerous and laborious, and we can expect that rather than traversing large swathes of the peninsula, traders would have stuck to a circumscribed area or else handed their goods off to local middlemen for distribution. In fact there are several possible scenarios by which these goods could have changed hands (Negroni Catacchio 1981: 144-145) has suggested periodic village feasts to which residents of other communities would attend). We may never know the mechanisms exactly, but we can say that the movements of these rare objects, such as amber or glass beads or Mycenaean style pots, would not have gone unnoticed, and the co-presence of the same exact fibula type at two nearby sites was not coincidental. Further I posit that these archaeologically visible movements of distinctive objects would have constituted the tip of the iceberg of interactions of all kinds between neighboring sites, and so the traces of the exchange networks index deeper social relations.

3The networks emerging from the study are regional in scale, with no unified peninsular network to speak of (Fig. 1). The regional groupings are of roughly equivalent size and spread around the peninsula. Some of these FBA regional groupings, such as the one in west central Italy (the future Etruria) and another in the Veneto, demonstrate high levels of connectivity, while others, such as the ones in Marche (Apennines) and Apulia, are weaker. The story plays out over the long term as through a process of path dependence, the structures of these earlier regional networks continued and apparently contributed to the later histories of the regions. The most connected networks in the FBA become cohesive groups in the Iron Age and after, while the weakly structured FBA networks do not (Fig. 2). While I have examined elsewhere these networks at the macrolevel, here I turn to one of the lower order components of the network, the triads (and by implication, the dyads), as a means of assessing in more detail the nature of the relations between nodes and more generally, transitivity.

Fig. 1

Fig. 1

Map showing networks

Fig. 2

Fig. 2

Netgraph of the six networks

Transitivity and Triads

4A central concept in network studies is transitivity. Transitivity pertains when all nodes in a triad are connected to each other. If A is tied to B, and B is tied to C, then the triad will be ‘transitive’ if A is tied to C, and ‘intransitive’ if A and C are not tied. From a theoretical perspective, the expectation is that transitivity will prevail, that ‘a friend of a friend is a friend’, or more specifically to the case study here, people from Site A will be willing to interact with Site C if A’s friends at Site B already interact with C. This is framed in network literature as the tendency to ‘close the triad’, and is seen as a feature of structural balance. Open triads with only two edges are labeled ‘structural holes’ and are thought to be unstable configurations. While this claim about the instability of structural holes has been empirically undermined (Burt 1992), there is still some value in thinking about the sociability of a network, through the clustering of ties. Further, calculating the transitivity of a network may be helpful for assessing the influence that these ties provide; in other words, the impact of a tie. If site B has so little influence on site A’s choice of trading partners, the ties between site A and B are perhaps not that consequential after all. Therefore, if we are to posit that the co-presence of these objects at the FBA sites really is something of significance, that it indexes deeper relationships between them, then we should expect relatively high transitivity among triads. In other words, the interactions between A and B should be such that A and C will also come to interact with each other. If, on the other hand, goods are moving around in a somewhat random fashion, perhaps by foreign traders with no real interest in which sites they offload their goods at, we may expect that transitivity between triads will not be particularly high. This question becomes fairly fundamental to a central premise of exchange studies in prehistoric contexts, therefore: that they are expressions of relationships of other kinds. There are thus two key questions that transitivity and the nature of triads may help answer for this particular case study: 1) to what extent do ties have an influence on the formation of other ties, that is, how strong was the tendency toward transitivity in these networks; 2) what do the differences in transitivity rates of the networks reveal about variations in the underlying social relations of sites in those regions? In what follows I will present a triad census and calculate the transitivity of six regional groups in Italy in the Final Bronze Age, compare the results, and assess their historical significance.

Case study

  • 1  See Blake 2014 for the complete data from this case study.

5The six groups in question include two in the northern subalpine region, the Garda group (seven nodes) and the Veneto group (eight nodes); two in central Italy, the Etruria group to the West (eight nodes) and the Apennine group (nine nodes) which spans the modern day regions of Marche and Umbria; and two in southern Italy, the Basilicata group (eight nodes) and the Apulia group (eighteen nodes) (Blake 2014)1. In a previous study I argued that the Garda group and the two southern groups were not the results of local agency so much as the traces of long distance exchange networks imposed by outsiders. The Garda group, I posit, was part of an even broader circuit that involved the Val d’Adige alpine pass, one of the main routes across the Alps, Lake Garda, and slightly further south. This may mean that the Garda network should be understood less as a local phenomenon and more as a segment of a longer distance transalpine route. We would therefore not expect much local influence in the structure of this network. The two southern groups, in the modern regions of Basilicata and Apulia, are likewise the results of the involvement of foreign groups in exchanges. Both networks are largely built on the distributions of Aegean pots (both imported from Greece and locally made using Mycenaean technologies), and the nodes are overwhelmingly coastal or subcoastal in placement. Whether Mycenaean traders established emporia along the southern coasts, or whether locals established the sites for the purposes of this overseas trade is an unresolved question (Blake 2008). The critical point here is that the networks seem to result from external ventures, not from the affirmation of local ties. In contrast, I have suggested that the other three networks are local phenomena, even if the objects circulating within them are exotica. The sites in the latter networks exhibit no coastal preference and in the Veneto and Etruria cases, at least, the networks map neatly onto later coherent ethnic groups, so the inference is that these networks were locally derived and then continued into later periods, evolving ultimately several centuries later into the named groups, the Veneti and the Etruscans. In the Apennine network, less clearly, the seeds of the Umbrians and Picenes may lie. However, this hypothesized distinction between local networks and externally derived networks has proven difficult to detect through a macroscale comparison. Densities don’t vary widely among the six networks and the posited ‘local’ networks do not look more cohesive than the foreign ones, by the standard measures (Blake 2014: Table 4.3). I turn therefore to a comparison of the local structures of these networks to see what this may reveal about the hypothesized distinction between locally driven and externally driven networks.

6To study transitivity the standard unit of analysis is the triad, composed of three nodes and the possible ties between them. A triad census tallies all the triads in a network, grouping them by triad type. While a triad census is more typically performed on directed networks, in which node A may be tied to node B and B may or may not be tied to node A, one can conduct a triad census of a non-directed network and still get substantive, if somewhat pared down, results. In a directed network, as developed in the work of Holland & Leinhardt (1970) and Davis & Leinhardt (1972), there are sixteen types of triads based on the combinations of ties between the three nodes. In a nondirected network, just four of these triad types apply. They are the null triad, in which there are no ties between any nodes (typically coded 003); the triad with a single tie, or couple (coded 102); the triad with two ties, or two dyads, often called intransitive (coded 201) and a triad with three ties, a complete or transitive triad (coded 300).

7Transitivity isn’t everything. Granovetter (1973) famously emphasized the importance of the weak ties extending out from transitive clusters in facilitating the circulation of new ideas and encouraging other relationships, and thus fostering some independence. Burt (2005) also notes that the node at the center of an intransitive (open) triad is in a very powerful position as mediator, who therefore may have no interest in closing the triad. So while we may no longer accept that closed triads are the expectation, or even the desire, we can nonetheless assess their presence.

8Faust (2006) has questioned the value of triad censuses in making comparisons between larger networks, suggesting that the character of triad census is largely determined by network density and by the character of the dyads: null, mutual, or asymmetric (in a directed network). Likewise, Goodreau and others have argued that transitivity tells more about dyadic relations, even if we study it through triads (Goodreau et al. 2009). It would seem then that dyads are the preferred level of analysis currently in network studies. It would seem that when we analyze triads we are really analyzing dyads. However one frames it, of interest here is getting at the local structure and a useful ‘way in’ is through the triad census. With these points in mind, we can examine the triad census in some detail. Figure 1 presents the tallies of each triad type for each network, followed by the transitivity of that network, which is derived by calculating the percentage of triads with two or more dyads that are complete triads. In other words, for each network, the transitivity is derived from adding the code 201 and code 300 totals and dividing that into the code 300 total: in the case of the Apennine group, for example, 18+4=22; 4/22=18.18%. But before we get to the significance of the transitivity calculations we can look at some of the other features of the triad census.

9What is immediately apparent is that in all cases transitive triads are in the minority among all triad types. This seems to suggest that there is no clear tendency towards clustering. But there are rather enormous differences between the network censuses too. Apulia stands out for its large size, which causes a high total number of triads and in particular, null triads and single tie triads. Apulia also stands out for being the only network in which the number of null triads exceeds the number of single tie triads and almost adds up to as many triads as the other three types combined. Also of note is that with the exception of the Veneto group, single tie triads outnumber intransitive triads in all the networks. This emphasis on ‘couples only’ relations within triads, in the historical context we’re focusing on here, suggests to me very weakly developed community identities and instead a focus on forging mutual one–on-one relationships between particular sites. The Veneto is exceptional here, and part of this may be due to the very centralized character of this network. One site, Frattesina, has ties to most of the other sites in the network, and was a dominant force shaping its local structure. This is the only network in the study that shows such a high tendency toward centralization. That the Veneto is exceptional in this regard is further reflected in its high transitivity score, discussed now.

10Transitivity ranges from a high of 35 % in the Veneto network to a low of 11 % in the Garda network. These are all relatively low, if one expects intransitive triads to be unstable. The transitivity scores thus at first glance reveal no strong tendencies toward closing structural holes, with far more two tie triads staying open than closing. This case does not seem to reflect relations needing closing. What does this suggest, in light of the hypothesis proposed earlier that if more relations than exchange were occurring along these paths, we may expect to see higher transitivity rates, as sites with ties already will have an influence on each other to make connections with third sites known to only one of the other two. That does not seem to be happening in a significant way here, and as suggested by the high numbers of single tie sites, I would interpret this to mean that these relations were not yet that intense. Put another way, the social impact of these exchanges of goods was not strongly felt yet in this period.

11But how about the second question posed earlier in this paper, regarding the differences between the hypothesized externally driven (I hesitate to say artificial) networks and the local networks? Individually, no pattern emerges, as Apulia, one of the networks I argue is external, has the second highest transitivity rate of any of the networks. But Apulia’s size seems to make its census results distinctive, with such a high number of null triads anyway. Instead, to mitigate against the individual differences, I calculated the mean of each group: the ‘externals’ (Apulia; Basilicata; and Garda) and the locals (Apennines; Etruria; Veneto). The mean transitivity of the external sites is 17.76 %, while the mean transitivity of the local sites is 26.7 %. This ten-point spread suggests that the ties between sites within the ‘local’ networks may have been more meaningful, in the sense of encouraging other ties, than the ties between sites within the local networks. As noted above, none of the networks demonstrate a strong trend toward transitivity so we should not overstate the results. In this early period of Italian history we must speak of networks rather than true communities. However, as I argue elsewhere (Blake 2013, 2014), these local exchanges of goods with neighbors may be the first signs of a dawning regional collective identity that would not crystallize for several more centuries.

12But it does not seem to have been enough to simply have goods moving between and among sites to trigger this identity: the sites in Apulia, Basilicata, and Garda were far from isolated from each other, and demonstrate similar densities of relations to the ‘local’ networks. But the peoples of Apulia, Basilicata, and Garda never coalesce into well-defined regional groups, while the residents of Etruria and the Veneto most certainly do. (The Apennine network is a somewhat special case as the FBA network spans two distinct groups, the Umbrians and Picenes, a phenomenon perhaps resulting from the peculiar features of this mountain environment and the apparent demographic mobility that prevailed there.) Instead, there must have been something about the significance of the locally driven exchanges that made them encourage group identity formation. In the different transitivity means we may be catching a glimpse of this: the preference for forging direct ties with sites with whom one already has an indirect connection. Contact (evident in the co-presence of objects) therefore was not sufficient to encourage collective identity-formation in a region. Microlevel decisionmaking mattered. Of course, establishing cause and effect when it comes to networks and identity can be tricky. Kitts & Huang (2010) note:

“Work in agent-based modeling has demonstrated that pervasive patterns in distributions of triads (such as transitivity) may be partly or wholly byproducts of social dynamics in dyads. A dyadic propensity toward homophily (e.g. choosing friends who are in the same social categories as you) will tend to foster transitivity, even if actors have no direct propensity to close triads.”

13This shifting of the causal force away from network ties to identity traits, essentially the opposite of what I argue, has important implications for the current study. If true, it suggests that the networks observed in the Bronze Age were already at least in part the result of regional self-identification, however inchoate. Either way, it is clear that the FBA is the formative moment for these regional groups, demonstrating greater continuities over centuries than previously recognized (e.g. Cornell 1995; Pallottino 1981).


14This paper has sought to add the analysis of local structure to the burgeoning field of archaeological network research. As noted above, local structure and how best to interpret it are the subjects of considerable debate in mainstream network scholarship. Incorporating analyses of dyads and triads into archaeological network studies with a long time depth may offer the opportunity for archaeologists to contribute to this debate.

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Ruffini G. 2008. Social Networks in Byzantine Egypt. Cambridge University Press, Cambridge.

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1  See Blake 2014 for the complete data from this case study.

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Table des illustrations

Titre Fig. 1
Légende Map showing networks
Fichier image/jpeg, 364k
Titre Fig. 2
Légende Netgraph of the six networks
Fichier image/jpeg, 321k
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Emma Blake

School of anthropology, University of Arizona, Tukson (USA),

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