Method update: beta-skeletons

This second update of the project’s method concerns the distance networks based on beta-skeletons described in an earlier blog post. We mentioned that the reconstruction of ancient trade routes is extremely complex as a number of variables should be taken into account, so our best bet is to focus on one parameter that might have been influential in determining trade routes. Using beta-skeletons and graph theory we will investigate whether the distance between centre of production and site of deposition is reflected in the ceramic evidence and whether it significantly influenced the selection of trade routes.

Although we mentioned in a previous post that the beta-skeleton would be compared with a reconstruction of trade routes based on the shortest path for every sherd from centre of production to site of deposition over this beta-skeleton, we now have to confess that this is nonsense as we would compare the beta-skeleton with a slightly altered version of itself that is based on a large number of assumptions concerning the intermediary sites. We realized that these shortest paths actually contain the hypothesis that we are testing, as they represent trade routes based on the ceramic evidence in which distance surpasses all other factors in importance.

To create such a network of trade routes we will make a beta-skeleton in which every site has at least one connection, so that all of them would be reachable. This will be done in ArcGIS with a beta-skeleton calculator programmed by dr. Graeme Earl, applied to all the sites in the database and their geographical coordinates. For every sherd the shortest path in geographical distance from centre of production to centre of deposition over this beta-skeleton will be calculated in pajek (although this can be done in ArcGIS, pajek is able to calculate geographical as well as graph theoretical shortest paths). Edge value will represent the number of sherds passing between two sites and edges with a value of zero will be discarded.

At this point we have a reconstruction of the trade routes over which the vessels would have been transported if the distance between start and ending point would have been the only factor taken into consideration by their transporters. This network embodies the hypothesis we want to test, which can be done by comparing it to another network visualisation of ceramic evidence. The networks of co-presence described in the previous post will provide this basis for comparison, as they do not contain any assumptions of their own (before their analysis that is).

Now, there is an obvious danger of comparing things with different meanings, so we need to be very clear of what aspects of both networks will be used for comparison. We will focus on a couple of phenomena that we think are represented in both types of networks: bridges and centrality.

A bridge is a line whose removal increases the number of components in the network (de Nooy et.al. 2005: 140). In our networks of co-presence a bridge is a site that forms the connection between two different groups of distribution networks. Such a site should play an important role in dispersing information on the pottery market as it is linked in with highly differing networks, but does not necessarily play a central role in the entire network. On the distance network these sites should play a similar role in connecting different distribution networks, in order for the hypothesis to be valid.

Sites belonging to the centre of a pottery distribution network can be easily reached by new pottery forms from diverse producing centres, they are central to the communications network of the pottery trade as it is represented in the ceramic evidence. This is true for both our shortest path network and our co-presence network, and can be measured using the closeness centrality method: sites are central in distribution networks if their graph theoretical distance to all other sites is minimal. In network terms: the closeness centrality of a vertex is the number of other vertices divided by the sum of all distances between the vertex and all others (de Nooy et.al. 2005: 127). Although this method will provide comparable numerical results (a score between 1 and 0), we will not compare these absolute values. Rather, we will focus on seeing whether sites that are central (or not) in our co-presence network are also central (or not) in our shortest path network.

Pairs of contemporary networks of both types will be compared using these methods in order to provide an answer to our hypothesis “was distance a significant factor in selecting trade routes?”

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