Table 1 contains eigenvectors sorted by order of their eigenvalue (first column). Each vector contains 942 elements, one per author. In Table 1 these are sorted by their absolute magnitude and only the name of the element and the values of the larger elements are given. Column 2 gives the number of elements displayed which, as described above, is the smallest number of elements needed to convey 90% of the eigenvector.
The first two eigenvectors are easy to interpret, cf. Fig. 6. All their large elements are positive and there are few of them. They summarise parts of the coauthor graph whose nodes (authors) do indeed collaborate and have many joint publications. However these provide only a summary of the interactions in both groups, as over time collaborative links might have been both strengthened and weakened. A single eigenvector cannot capture all of this information. Instead, as we shall see later, other eigenvectors strengthen and weaken links established earlier, so that the collaborations are represented with greater precision.
If we start at the top of Table 1 we can reconstruct our field in increasing detail. Each time we consider a new eigenvalue/eigenvector pair the resolution is improved.
The third eigenvector (Fig. 6) has four positive elements, corresponding to four collaborators but also a negative element (RP −0.17). The negative element does not mean that this author does not collaborate with the others. When we add the third eigenvector, we add four nodes (and up to 28 new links) but by the time of the third eigenvector there is overlap with the two larger eigen components. The negative value indicates the third eigenvector represents a tight group of four collaborators and that the collaborative links with one of the existing nodes in the reconstructed network must be weakened.
The fourth eigen component, is an example where most of the eigenvector’s large components are negative. However there is one element (RP 0.13) with a large positive value, indicating that the overlap between this group of co-authors and the existing graph must be reduced for this element, rather than increased.
Most of the large elements of the fifth eigenvalue are positive whilst the largest is negative. Perhaps this can be thought of best, not as collaborators of the first author (WBL −0.71) but of the second (RP 0.60), where, again, the sign reversal indicates not that these two coauthors do not collaborate but that the links already established by the second eigenvector must be adjusted. Note one author (BB −0.09) has not collaborated with the second author but with the first and so his eigenvector element has the same sign as the first author and the opposite of the second.
The next four eigenvalues all have large elements of the same sign. Each represents an important collaboration in our field.
The tenth eigenvector (David Andre) is again of mixed sign and represents an important readjustment of the collaborative links. Most of the large elements represent adjustments to links between John Koza’s coauthors and the addition of five of his coauthors who were not among the major component of the first eigenvector. Secondly, elements PN 0.22, WB −0.14 and HI −.08 adjust links between coauthors in the third and seventh eigenvectors.
The eleventh eigenvector (Peter Nordin) can be thought of as similar to the fifth. It, too, contains a mixture of positive (PN) and negative (WB) values. The positive elements creating links between PN and important collaborators, whilst the negative ones mostly create new links for WB. While others appear to be making modest adjustments to existing members of the graph. Note some links are established by collaborations on coediting conference proceedings.
The twelfth eigenvector is the first one to contain many large elements (32). Many of these (which are all of the same sign) represent collaborative links established by Una-May O’Reilly through coediting Advances in Genetic Programming, EuroGP, GECCO and Genetic Programming Theory and Practice. Others represent collaborations on papers.
The next eigenvector has all positive large elements and introduces Jason Daida and his collaborators. The fourteenth summarises the collaborations of Maarten Keijzer (note the data are prior to the publication of GECCO 2006, which he edited). However, two opposite sign elements (CR −0.16 and JFM −0.11) again indicate adjustment to existing links. The fifteenth eigenvector also contains many large elements (18). These are mostly the collaborators of Lee Spector. Again elements with the opposite sign suggest adjustment to the existing network (particularly for John Koza’s coauthors and those introduced by the previous eigenvector). While one element (JBP 0.05) represents the addition of a coauthor of a coeditor (PJA 0.10) of Lee.
Ten of the remaining 28 large eigen components have relatively few large elements and these are mostly of the same sign. They can be thought of as mostly describing an important group of collaborating authors. Other eigenvectors tend to have more large components with more evenly matched number of positive and negative elements. While they introduce new authors they also play an important role in adjusting strengths of existing links.
The two eigenvectors for Tom Hayes have similar eigenvalues (\(\approx 43\)) and are relatively diffuse (15 and 20 major elements) but 12 authors play major roles in both. Again positive and negative values appear, indicating these two eigen components play an important role in recording the asymmetry in the graph. Similarly the pair of eigenvectors for Nick McPhee (60 and 40 components) both have eigenvalues of about 27 and have 35 coauthors in common. The mix of signs indicates the formation of clusters with strong links within a cluster but no or weak links between strong centres.