Structural properties of temporally specific networks

Hub and authority scores (Kleinberg, 1998) are particularly suited for studying the patent networks considered here. Two weights were computed for each vertex, one for hubs and one for authorities. A good hub is a vertex in a network with many good authorities pointing to it and a good authority is one pointing to many good hubs. Let A/" = (V, L, w) denote a directed network with weights on lines. V represents a set of vertices, £ a set of lines, and w : £ -"• R. For every vertex v GV, two weights, hv and av, were constructed. The hub score, hv, for v is given by

Hubs and authorities weights for categories over time. The authority score, av, for v is obtained from

Figure 5.8 Hubs and authorities weights for categories over time. The authority score, av, for v is obtained from

An iterative method for establishing hv and av computes the principal eigenvectors of matrices WrW and WWr where W is the adjacency matrix of the network. (See Section 2.11 for more details on hub and authority scores.)

Figure 5.8 shows the temporal distribution of the hub and authority scores for the six technological areas. Hub scores are on the left with authority scores on the right. The order of hub scores at the first time period is mechanical, E&E, others, C&C, chemistry, and D&M. Thereafter, the temporal trajectories differ dramatically. Both C&C and E&E have reversed fluctuating trajectories. However, both have the highest hub scores among the technological categories in 1999. Hub scores for mechanical drop until 1992 before climbing to finish with the third highest value in 1999. The other three technological areas have hub scores declining throughout this period and finish at the bottom three levels. D&M ranks the lowest throughout, consistent with being less well linked to the other technological areas.

Viewing the right panel of 5.8 shows only C&C and E&E as having higher authority scores in 1999 compared to 1987. In the main, all authority scores for the other technological areas decline. The fluctuations for C&C and E&E are reversed in this panel. Further, they are reversed compared to the changes in their hub scores. These plots appear to supplement the results shown in Figure 5.7. Overall, the important hubs are mechanical, C&C, and E&E. Both C&C and E&E became especially influential over the last quarter of this interval. The other three technological areas lost some of their importance. The picture is similar for authority scores. However, E&E was by far in the best position in 1999, while C&C gained advantage towards the end of this period compared to mechanical, chemical and others. Kejzar (2005) suggests that authorities represent technological categories playing an important role in setting the base for the other areas. Large hub values correspond to categories drawing upon many other technological areas. This clarifies the initial place of E&E and the late rise of C&C. These results help to account for the huge boom for C&C in the 1990s due, most likely, to the development of the Internet. D&M depends primarily on chemical in all panels of Figure 5.7, especially for 1999-2006. As a result, both its hub and authority scores are small throughout this period.

The flows presented in Figure 5.7 used the actual patent citation flow data. However, Figure 5.6 shows the six technological categories differing in terms of the numbers of patents they contain. This raises a simple question: how much do patents from their technological areas cite patents outside their areas relative to their sizes? To respond to this query we used relative citation frequencies. These line weights wl(jet) were calculated from

For a line / ee (u,v) e £ where u,v gV, pu denotes the property of a vertex u. To explore the role of these relative citation weights, we did not simply repeat the analysis shown in Figure 5.7. From Figure 5 .6, the start of a steep increase in the number of patents for categories begins in 1996. It made more sense to focus attention on the period after 1996. We note also, following an inspection of networks prior to 1996, that the difference between using simple and relative weights was negligible. Paying close attention to the period 1996-2006 provides an opportunity for a more detailed use of the sliding window technique.

Figure 5.9 shows the between-technological areas networks for 1996-2003, 1997-2004, 1998-2005, and 1999-2006. As before, the sliding window has a width of eight years: each pair of successive networks has seven years in common. This permits more short-term comparisons than were made in Figure 5.7. In the following, we make two comparisons. One features the four networks shown in Figure 5.9 while the other focuses on the 1999-2006 panels of Figure 5.7 and Figure 5.9.

The dominant features in Figure 5.9 are the reciprocated relative flows (w^rer)) between C&C and E&E, as was the case for the actual flows in Figure 5.7, but with attention on a narrower time frame. Little changes from 1996-2003 to 1997-2004. For both (overlapping) periods the relative patent citation flow from C&C to E&E is higher than the reciprocal flow. This is reversed for 1998-2005; the change was dramatic. The sizes of the relative flows between C&C and E&E for 1996-2006 reverts to the pattern of 1997-2004, suggesting that something important occurred between 1997-2004 and 1999-2006. This impression is reinforced by the heavier citation flow from E&E to mechanical for 1998-2005, given that the flows between these two technological areas were close to parity for all other periods.

The third highest relative citation flow for both 1996-2003 and 1997-2004 is from D&M to chemical. The reciprocal flow is far weaker. However, the citation flow from D&M to chemical drops dramatically in 1998-2005. This citation flow strengthened for 1999-2006 but remained well below the levels of the first two networks in Figure 5.9. The reciprocal flow from chemical to D&M changed little across the four periods. Two other changes in the pattern of the relative citation flows in 1998-2005 are noteworthy. The relative flow from E&E to chemical is largest in this period and is the fourth highest. While considerably smaller, the flow from E&E to others is also highest in this period.

Changes in the structure of patent citation networks can occur for several reasons including: 1) shifts in the volumes of patents across technological areas; 2) unusually large increases in the number of citations from patents in one technological area to patents in another area in a time interval; and 3) changes in USPTO procedures for processing patents. Looking at the total citation flows, as in Figure 5.7, focuses attention on citation volumes alone. When

Shrunken networks in the four time windows for relative citation flows.

Figure 5.9 Shrunken networks in the four time windows for relative citation flows.

Loops were removed. Given the sizes of the flows, line values were multiplied by 0.05 for a more readable figure.

relative citation flows are used, some control of differential numbers of patents by technological areas is imposed. The overall features discerned from Figure 5.7 are not contradicted by the results in Figure 5.9. However, there were subtle shifts in emphases when relative citation weights were used. We suggest using both types of patent citation flows for assessing this kind of temporal change to obtain a more nuanced assessment of structural changes.

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