‘Trade beads and bead trade’ - digitally remastered

As explained, the data analysed in ‘Trade beads and bead trade’ represents a highly appropriate material for network analysis. The entire dataset of the study is presented as a catalogue with detailed information on the beads and other finds in each grave assemblage. This data is digitized for the present study in order to compare the original analysis with a computerized network analysis.

The geographical distribution of the archaeological contexts are spread across Scandinavia. In the map (Figure 7.5) the size of nodes corresponds to the number of beads in a context, ranging from a typical figure of 10-40 per grave to a small number of very abundant contexts with more than 200 beads. The finds clearly cluster in certain regions. In particular, there are 87 recorded graves - more than a quarter of the whole dataset - from the trading town Birka in Middle Sweden. While Birka was a centre of a densely populated region, and some other parts of Scandinavia were more sparsely populated, it is clear that other regions are not equally well represented. There are few finds recorded from Denmark and Southern Sweden, and two small but significant regions, Gotland and the Aland islands, are not considered for the study (cf. Callmer 1977, 7 and 10).

In order to enable a formal network analysis, the association of bead types and contexts is digitized and visualized as a two-mode network with 916 nodes (bead types + contexts) where bead types are shown as dark gray nodes and contexts (graves) as light gray nodes (Figure 7.6). The scale of nodes corresponds to their degree centrality (i.e. the number of contexts per bead type, resp. bead types per context). The layout is generated using

Figure 7.5 The geographical distribution of 302 archaeological contexts with >10 Viking Age glass beads. The size of nodes corresponds to the number of beads in a find. Digitized after data in Callmer 1977.

Figure 7.6 The association of bead types and contexts in Callmer (1977) visualized as a two-mode network. White nodes: bead types. Black nodes: contexts (graves). The size of nodes corresponds to their degree centrality (number of contexts per bead type resp. bead types per context). The layout is generated using the VOS Mapping algorithm of the Pajek software package. Graphics: Pajek and S. Sindbrek.

the VOS (Visualization of Similarities) Mapping algorithm (Waltman et al. 2010) and the Pajek software package (de Nooy et al. 2018).

VOS was originally developed for community detection in bibliometric research, but lends itself well to other forms of affiliation data. Whereas network analysts have often used separate algorithms to define groups and to visualize similarities (e.g. Sindbæk 2010), VOS has the advantage of using the same integrated algorithm for both clustering and topological mapping. Compared to other techniques for detecting clustered groups in network data, such as block-modelling, multidimensional scaling or mapping techniques, VOS has been shown to be less prone to produce artificial patterns (‘artefacts’), and to yield a generally more satisfactory representations of datasets (van Eck et al. 2010).

In the graph Figure 7.6 the data in the VOS algorithm calculates the position of nodes to produce a measure of relative similarity of nodes in a network. Nodes with very different connections appear far apart in the graph, while nodes with strong similarities cluster in the same region. Densely connected nodes draw towards the middle of the graph and sparsely connected nodes towards the periphery. The graph reveals a relatively sparse and evenly distributed set with no conspicuous hubs or cliques. The relations are widely distributed: the network is not held together by a few hyperabundant bead types - rather, there are more than 60 bead types which occur in more than 20 different contexts. The network has 3098 links in total, and a density of 0.025 (i.e. 2.5 percent of all possible lines are present). This is a fairly typical score for a social network of this size, and suitable for many forms of analysis (de Nooy et al. 2018, 76). The average degree is 8.75, and the degree variation ranges between 1 and 122 (the latter being the maximum number of assemblages in which the same bead type occurs). A special phenomenon can be seen at the margin of the graph where rare bead types that occur only once are shown. These often occur in find-rich assemblages, whence some of these (shown as relatively large, yellow nodes) are also drawn towards the outer parts of the graph.

In order to asses Callmer’s classification of beads, the two-mode network is reworks as a one-mode network: the nodes representing assemblages are removed and replaced by links between every bead type linked to that node/assemblage. When represented in this way, the graph becomes visually very dense. By analysing nodes of only one mode, however, we are able to apply more adequate analytical tools to search for structure.

The one-mode network now consists of 406 specific bead types, which Callmer has classified as 54 bead groups. To test the validity of this classification, we add a separate ‘partition’ list, where each individual bead type is assigned to the relevant group. We remove bead types that are not assigned to any group, as well as rare bead types, which are not linked to any other types.¹ Two rare bead groups, which are unrelated to other groups, are similarly excluded. The resulting network has 382 bead types assigned to 52 bead groups. Using again the VOS mapping algorithm we can now map the relative affinity of these groups (Figure 7.7a). The resulting graph shows the bead groups separated by shades and marked by numbers from 1-54. Callmer labels the groups Aa, Ab, Ac, Ba, Bb, etc.; for convenience they are numbered here, but follow his order of presentation. The individual types are labelled using Callmer’s type codes (e.g. B408, E140, etc.). The graph shows clustering among beads types in some bead groups, but for many others there is no visible association. Rather, the shape of the graph suggests that other relations are present.

To complement the mapping we can use the clustering function of the VOS algorithm to suggest how the set could be split into groups on purely formal grounds. The algorithm can be set to separate the nodes into many or few groups depending on the ‘Resolution Parameter’. Setting this to 1.0, 18 groups appear (Figure 7.7a). They comprise three groups (16, 17 and 18), which consist of one bead type each. These are types, which associate so differently to all other groups that they are statistically more properly sorted as singular outliers than grouped with any others. The remaining 15 groups include between 8 and 46 bead types. Most of these show a tight

Figure 7.7 The association of 382 bead types in Callmer (1977) visualized as a one-mode network. Links indicate occurrence in shared assemblages. The layout is generated using the VOS Mapping algorithm of the Pajek software package. In a) the nodes are shaded and labelled according to Callmer’s 54 general classes or bead groups; in b) the shades and labelling correspond to 18 groups defined by VOS clustering (resolution parameter = 1.0). Graphics: Pajek and S. Sindbsek.

Figure 7.7 Continued

A complex beadwork 161 clustering in one region of the graph, suggesting that the groups express robust patterns in the data.

We may compare the result of the VOS classification to Callmer’s bead groups directly by re-coding the two sets of classification as a two-mode network in which Callmer’s groups constitute one mode of nodes and the VOS groups the second. A bead type assigned, for example, to bead group no. 25 in Callmer’s classification and to group 5 in the VOS classification will mark a link between these two classes (Figure 7.8). Many of Callmer’s groups appear to be randomly connected among several VOS groups, suggesting that the individual bead types assigned to them do not associate closely in assemblages. Some notable exceptions stand out: Group 43 (segmented beads, class E) and 44 (cut, drawn beads, class F) both have a strong correspondence to VOS group 11. The VOS algorithm associates these two bead groups, and separates both from the rest of the set. Group 45 (composite mosaic beads, group G) corresponds similarly closely to VOS group 8, which, moreover, show a strong link with bead group 14 (dark blue monochrome, wound beads). This confirms a well-known chronological pattern, according to which composite mosaic beads are associated with a ‘blue period’ of beads. A last, very prominent correspondence is seen between groups 51 and 52 (rock crystal and cornelian beads) and VOS group 13. The stone beads cluster very strongly, and associate less often with other bead types.

Although Callmer’s bead groups do not all display coherent clustering, they are based on well-reasoned, typological generalization. Many of the 406 bead types represent minor variations in shape, size, color, etc. Beads produced by one bead maker in the same batch might come out as half a dozen different types in this classification. When split into many subtypes, as in the analysis above, they will only trace links to exactly the same sub-type of bead. Associations might come out differently if we accept the 54 general, typological bead groups as a basis of analysis. We can test their coherence using another approach in Pajek.

To explore this, the network of 382 bead types is reduced (‘shrunk’) to Callmer’s 54 bead groups. In this operation, the multiple Bead Types in each bead group are combined to one single node, which sums up the relations of all bead types in the group. This network is displayed using VOS mapping, and split into groups defined by VOS clustering with various parameters (Figure 7.9). The resulting graph displays clear patterns, consistent with trends noted above. The two major import types, the segmented (bead group 43) and cut (bead group 44) beads are united in all versions. In Figure 7.9c they form a small VOS group together with another characteristic type of imported beads, mosaic eye beads (bead group 46), an association which makes excellent sense in terms of known chronological patterns.

In the same graph, another group captures an equally distinct set of types: Blue monochrome (bead group 14), monochrome greyish green

Figure 7.8 Associations between classes of beads in Callmer’s 54 bead groups (outer circle) with 18 groups (inner circle) defined by VOS clustering (cf. Figure 7.7). Lines indicate bead types shared by a class in Callmer’s classification and a VOS cluster. Multiple associations are indicated by wider lines. Graphics: Pajek and S. Sindbtek.

Figure 7.9 a) The same network as in Figure 7.7 reduced (‘shrunk’) to Callmer’s 54 bead groups. Each class of bead types is reduced to one node, which sums the relations of all bead types in the group. Nodes are labelled according to Callmer’s 54 general classes or bead group. Shades correspond to groups defined by VOS clustering, with various parameters, a) Resolution Parameter = 3.0, N clusters = 32; b) Resolution Parameter = 2, N clusters = 22; c) Resolution Parameter = 1.5, N clusters = 13; d) Resolution Parameter = 1.0, N clusters = 6. Graphics: Pajek and S. Sindbtek.

Figure 7.9 Continued

(Bead Group 23), blue with white and read trail decoration (bead group 29), beads with reticelli (twisted rod) decoration (bead group 33), composite mosaic beads (bead group 45), ‘frosted’ opaque rock crystal beads (bead group 50) and amethyst beads (bead group 53). All these are known from stratified excavations to be associated with the earliest phase included in this dataset, Callmer’s Bead Period I (Feveile and Jensen 2000). These and other patterns suggest that the bead groups are relevant tools for classifying the set.

When a two-mode network is reworked into one mode, we can choose to look at either of the original two modes as nodes. Above, we have considered the bead types connected by joint occurrence in assemblages. We can shift mode to analyse the same data as a complementary network of bead assemblages linked by the shared bead types (Figure 7.10). As is often the case when a two-mode network is converted to one-mode, the links become a dense mesh. The size of nodes corresponds to their degree centrality (number of bead types per context), while the shading of the lines indicates the strength of ties (darker lines indicate more shared bead types). The nodes are labeled according to Callmer’s twelve main groups of assemblages. VOS mapping is used again to map the relative similarities of the nodes. Most of Callmer’s Bead Periods can be seen to cluster fairly tightly in one area of the graph. Two groups are notably fuzzy: Bead Period 3, characterized by small cut, tubular beads (red nodes); and Bead Period 9, characterized by segmented beads of mainly yellow or green glass. These two groups spread over a wide area of the graph, suggesting that they are not well-defined clusters within the set.

We can explore the classification again using the VOS clustering algorithm. This search can be calculated on the basis of the weight of links, i.e. the number of individual, similar beads between every assemblage. In the present data, however, this can be shown to lead to strongly skewed results because of the highly uneven total number of beads. In particular, the small cut beads, which define Callmer’s Bead Period 3 and 6 tend to occur in very large numbers in the assemblages where they are found. This is the case, for example, for the two assemblages with the highest number of beads recorded: a grave with 1216 beads from Harbartholmen, Steigen Parish, Norway (T5281), and another with 603 beads from Jarvsta, Valbo parish, Sweden (SHM 28025:24C), both consisting almost exclusively of small cut beads. The number of beads in these graves is a simple reflection of their tiny size, which implies that many beads are needed to cover any length of string. Yet when compared to assemblages with larger and less numerous beads, the huge number of shared beads in these and a few other finds will stand out as an extremely strong cluster.

It is necessary for a meaningful comparison, therefore, to ignore the number of individual beads, and consider the number of shared bead types. For resolution parameter = 1.0 VOS returns five with a fairly robust division (Figure 7.11a). If we compare this division to Callmer’s groups we find

Figure 7.10 The association of 296 bead assemblages in Callmer (1977) visualized as a one-mode network. Links indicate shared bead types, multiple associations indicated by darker shading. The size of nodes corresponds to their degree centrality (number of bead types per context). Nodes labeled according to Callmer’s groups. The layout is generated using the VOS Mapping algorithm of the Pajek software package. Graphics: Pajek and S. Sindbrek.

no strict correspondence, but there is a marked tendency for three of the five clusters to coincide with assemblages dominated respectively by wound beads (I and VII), segmented beads (II and IX) and stone beads (IV, V and VIII). This confirms Callmer’s proposition that these material type groups are important vectors of the set.

If we explore different settings, we find that a resolution parameter =1.5 yields a total of 20 clusters, of which a number, however, are cliques of only one or two assemblages (Figure 7.11b). Considering the nature of the dating set, it is intuitively plausible that outlying cliques should occur, as evidence of assemblages brought together by unusual circumstances.

Figure 7.11 The association of 296 bead assemblages in Callmer (1977) visualized as in Figure 7.7, but with clusters defined by the VOS algorithm with two different settings: a) Resolution Parameter = 1.0, VOS Qual. = 0.25584, N clusters = 5; b) Resolution Parameter = 1.5, VOS Qual. = 0.17361, N clusters = 20. Graphics: Pajek and S. Sindbtek.

Among the remaining groups thus defined, five show a very strong correspondence with Callmer’s groups. This can be demonstrated with reference to a graph showing how bead assemblages are correlated between the two sets of classification (Figure 7.12). The size and shading of the lines are scaled relative to the number of shared contexts (thicker line/darker shading = more shared contexts). For clarity, links with a weight of less than 5 shared contexts are omitted. This comparison reveals that five of the VOS clusters in Figure 7.11b show a strong correspondence to groups in Figure 7.7: I - Cluster 8; III - Cluster 4 and 13; VI - Cluster 10; VII -Cluster 3.

The correspondence confirms that Callmer’s groups I, VI and VII are rightly identified as clusters in the set. For the remaining groups, the relationship is more ambiguous. Ill (dominated by cut, tubular beads) may be better analysed as two or three distinct groups. II and IX (both defined by a ratio of >49 percent segmented beads) are both strongly associated with cluster 1 (yellow), but are also linked with other clusters. This could suggest that assemblages with segmented beads have much in common despite chronological spread. The same is the case for IV, V and VIII, all marked by a strong proportion of stone beads. The graph suggests that assemblages with stone beads cluster strongly, and are not easily divided into two distinct, chronological groups. Rather, they appear to form a distinctive group of ornaments used over an extended period of time. Finally groups X and XI are not well defined but cluster with other groups, as Callmer also notes in the course of his analysis (Callmer 1977, 65).

Callmer BP 7

Figure 7.12 Comparison between Bead Periods in Callmer (1977) and clusters defined by the VOS algorithm in Figure 7.11b. Five clusters (3,10,13, 4 and 8) show a strong correspondence to one Bead Period each, while the remaining four have an ambiguous association. Graphics: Pajek and S. Sindbiek.