Method update : co-present forms and wares

In a previous post we described how a network analysis of co-present forms and wares might help us understand the distributions evidenced by the ceramic data. Here we will elaborate on this type of network by explaining how we will create the network, what it represents, how we are planning on analysing it and what the results of our analyses actually mean.
At the basis of our analysis lies a two-mode network: a network in which vertices are divided into two sets, and vertices can only be related to vertices in the other set (de Nooy et.al. 2005: 103). In human language, sites are connected with forms/wares that are present on the sites, and the forms/wares are themselves connected to other sites on which they were found. A fictitious example of a two-mode network is given in figure 1. A major benefit of using two-mode networks is that we do not lose any information present in the dataset, the specific forms and numbers of sherds present in specific sites are represented in all their complexity. The data will be extracted from the project’s database to form such two-mode networks.

Fig. 1: A fictitious two-mode network representing sites connected to pottery forms which are present on the site. The value indicates the number of sherds of a form that have been found. (click to enlarge)

To facilitate the analysis of the data, however, we need to transform this two-mode network into two distinct one-mode networks. This is done for the example network of figure 1 and represented in figures 2 and 3. Both one-mode networks provide us with a different type of information: the first one (Fig. 2) represents the sites as vertices connected by the number of forms that are present on both sites; the second one (Fig. 3) represents the forms as vertices connected by the number of sites on which both forms are present. The strengths of a visualisation of ceramic distributions as networks should already be apparent in these one-mode networks.

Fig. 2: A fictitious one-mode network representing sites connected to sites which have evidence of the same pottery forms (co-presence). The value indicates the number of pottery forms that are co-present. (click to enlarge)

Fig. 3: A fictitious one-mode network representing pottery forms connected to other pottery forms which have been found on the same site (co-presence). The value indicates the number of sites on which both forms are co-present. (click to enlarge)

Now, what do these networks actually mean? As it is our goal to shed light on the relationship between ceramics and the dynamics of Roman trade, we should be very critical and clear about this point. We state that when sites have evidence of a specific pottery form in common, they have a connection of some sort. The nature of this connection represents, in its broadest sense, the distribution network of a pottery form. What network analysis allows us to do is to analyse the structure of these distribution networks, which will help us understand the processes that reach, maintain and evolve these structures.
A first step in our attempt at understanding the structure of Roman ceramic distributions lies in identifying strong components using m-slices (de Nooy et.al. 2005: 109-113) : we will look for vertices which are strongly connected to each other and have high edge values (ie. number of sites or co-present forms). For the first one-mode network (Fig. 2) such a strong component will contain sites that are all part of the distribution networks of a variety of pottery forms. In this fictitious example Athens, Rhodes and Sparta all have evidence of the same two pottery forms (EAA1 and EAA2), which might lead us to conclude that similar processes led to the deposition of these specific sherds on these sites. For the second one-mode network (Fig. 3) the strong components indicate pottery forms that are present in the same sites and, therefore, have a similar distribution pattern.
Such an analysis might considerably improve our understanding of ceramic distributions as it allows us to answer questions such as: What pottery forms had a similar distribution? Can this be explained by the proximity of the producing centre to the consuming sites? Is there a significant difference in the distribution of pottery forms made from the same ceramic ware group (ie. the same producing region)? Is there a similarity between distribution patterns of forms from different wares (which might indicate similar processes of distribution for different producing centres)?
Apart from identifying clusters of sites that form part of similar distribution networks and pottery forms that had a comparable distribution, we can examine the position of individual sites in these networks. When we restrict our attention to the connections in the networks, we get an impression of the diversity of trade relations. Every edge represents the membership of a site or pottery form to a distribution network. Vertices with many edges have access to many and diverse distribution networks, which might indicate better knowledge of trade patterns or a stronger position in pottery trade, as more information on pottery distribution networks is at their disposal. Such aspects can be studied by focusing solely on the number of absolute or relative edges, using methods to define degree, K-cores, closeness, betweenness, bridges and week ties. Although we can’t elaborate on their exact application here, these measurements help us understand the position and roles of sites and pottery forms in different distribution networks. We might be able to identify sites which played a dominant or regulating role in the distribution of specific pottery forms or wares. We would like to stress that identifying such sites is crucial in any attempt to reconstruct trade routes, as they might serve to fill in the gaps on a transportation route from producing centres to consuming centres.
Another strength of our approach will lie in the analysis of networks from different time periods, allowing for the evolution of distribution patterns to become apparent, and threshold periods to be identified.
This type of networks will form the basis for a comparison with contemporary shortest-path networks, described in the next method update.
The analysis of the structure of the distribution patterns as they are represented in the co-presence networks will be studied in more detail using hierarchical clustering based on dissimilarity measurements. This refinement of our method will be described in a later blog post.

Co-presence of forms and wares

Our previous post mentioned the issues concerning the definition of non-geographical networks. In this blog post we will give an example of such networks, and how it might lead to interesting insights about pottery distributions.

The production centres of major eastern table wares range from a limited number of cities (e.g. Eastern Sigillata C (ESC)) to a more widespread regional production (e.g. African Red Slip Ware (ARSW)). Each centre produces fine wares with a specific fabric, making it possible to differentiate their distribution patterns. Such distributions might be visualised as networks in which sites are the individual nodes and the relationships between sites represent the number of wares (not sherds) that are present at both sites at the same time-period. This would provide a series of very simple but rather informative networks representing the sites involved in the distribution of a specific table ware, which can be compared and added up with the networks of all other wares and analysed through time in 15-year periods.

These networks might provide useful insights on the relationships between cities and most importantly people, who were involved in inter-regional ceramic trade.

Another approach focuses on the individual forms which, in contrast to the general distinctions between producing centres, presents us with a different type of information going back to the individuals producing the pots and the people for whom they are made. In addition, a single form can be produced in several centres and in different table ware fabrics, allowing for the rise and fall in popularity and the diffusion of pottery forms to be analysed. A network of pottery forms represents sites related to each other on the basis of the number of forms they have in common in a specific period.

Such networks allow the study of the distribution of individual pottery forms, to group sites based on the simmilarity or difference of their pottery assemblages, and to see the evolution of these disstribution patterns in 15-year periods.

The two non-geographical networks described above might form the basis for discussions around the following topics: are the distribution patterns of individual forms dependant on/similar to the existing inter-regional socio-economical networks of major fine ware distribution? Do forms that are produced in multiple table ware fabrics circulate in networks that are similar to one or more of these wares? Are form/ware networks linked to social networks of potters, traders, land owners and how can we distinguish between the actors in pottery trade?

An important issue we need to raise, however, is that in the above networks we only used the number of co-present wares/forms rather than the number of co-present sherds. Although we might avoid the bias of archaeological research interests and emphases in this way, we might also miss a chance of having an indicator of the intensity of distribution as represented in the sheer volume of sherds.

The above networks can be tested on their validity by confronting them with their socio-economic and political framework (Bes 2007). We have not yet figured out a way to test these hypotheses quantitatively.

Any comments on these networks, the questions they might answer or the very nature of this approach are more than welcome!