Belen Kinship and Marriage Network

This graph shows the largest connected component of Belen nuclear families and their ancestors as vertices, with male descent lines linking parents' to sons' marriages as arrows between vertices and intermarriages between families as undirected edges. Vertices representing current residents are numbered according to relative wealth or economic position: 1 Economic elites 2 Well-off 3 Average means 4 Poor . The graph is drawn by a spring embedding algorithm that draws cycles of connection to the center of the graph. Three features of the graph are striking:

(1) The 26 shortest elementary cycles are long; none are short

(2) Families do not cluster in the center but are spread out along the edges in cycles of very large diameter or as points connected to the cycles

(3) The families of rank 1 and 3 tend to occur more frequently in the cycles than in the peripheries of the graph. When you return to the previous page, note the contrast with the next graph, that of the compadrazgo network, which is drawn with the same spring embedding algorithm but has a starkly higher concentration in the center of the graph.

These 3D drawings are made with the downloadable network program Pajek. The following diagram shows five generations (six counting the few white ancestors); those in the lowest (yellow) generation are usually relinked by generations 3-5 (we see some relinkings for the purple vertices in 5). Here in each generation we can see the same pattern as above: the families are linked in large circles of long-cycle marital relinkings, not in close clusters. There are what appear to be family clusters as well. The following figure represents the same data, but this time the algorithm adds the extra distance between generations, so the scaling pulls together those who are lineally related into closer clusters. Note the structure of long cycles is no longer so visible. All the images including this one are exported from Pajek in extended PostScript (eps), read into Ghostview, copied to MS NotePad and then pasted to Paintshop where colors were adjusted and finally saved as jpg files; some of the images that follow were exported in eps and read by HiJackPro which saved them to jpg files. The bi-components option in Pajek (like the original pgraph programs) allow us to select out ONLY the bi-components or marriage relinkings, as shown in the following diagram. Note that the spring embedding has found the core to have various embeddings of more closely related families whose common ancestry varies accordingly in time. In Pajek, remember, this image is 3D and can be spun in any dimension. The next image shows how, of the 138 couples in this remarriage block, where every couple is relinked with every other, 133 are or were residents of the town of Belen as opposed to ancestors from other villagers. Even if we remove these five, the size of the remarriage only shrinks by a few more couples who were relinked through the outsiders. When running in Pajek the 3D diagrams also can be rotated, and the vertices recede in size according to distance, so the 3-dimensionality of the image is more visible. Caution: this virtual reality walkthrough of the 3D graph image, made by Pajek, is an experiment requiring Cosmo Player, a Netscape Navigator plug-in; it may tie up your machine for some while (it did mine but not my son's), so best use it only with super-fast machines (Java script is still pretty slow since it is an interpreter language). HiJackPro reads this file but is equally slow, so it is better to edit large 3D images within Pajek (where points and lines can be moved and colors edited by changing their partition numbers) and not within these 3D image processors. Give the 3D image technology some time and these large datasets will be viewable as walkthroughs of the internal structure of the linkages along with labels for the vertices.