Topology and evolution of technology innovation networks

Sergi Valverde, Ricard V. Solé, Mark A. Bedau, and Norman Packard

Phys. Rev. E 76, 056118 – Published 28 November 2007

Abstract

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here we study the patterns of change of patents registered by the U.S. Patent and Trademark Office. We show that the scaling behavior exhibited by this network is consistent with a preferential attachment mechanism together with a Weibull-shaped aging term. Such an attachment kernel is shared by scientific citation networks, thus indicating a universal type of mechanism linking ideas and designs and their evolution. The implications for evolutionary theory of innovation are discussed.

Received 2 December 2006

DOI:https://doi.org/10.1103/PhysRevE.76.056118

Authors & Affiliations

Sergi Valverde¹, Ricard V. Solé^1,2, Mark A. Bedau^3,4, and Norman Packard^2,4

¹ICREA-Complex Systems Lab, Universitat Pompeu Fabra, Dr. Aiguader 80, 08003 Barcelona, Spain
²Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
³Reed College, 3203 SE Woodstock Blvd., Portland, Oregon 97202, USA
⁴ProtoLife, Parco Vega, Via della Liberta 12, Marghera 30175, Venice, Italy

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Vol. 76, Iss. 5 — November 2007

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Images

Figure 1
From (a) to (f), evolution of the computed tomography (CT) patent network. This is a subgraph from the full USPTO patent network. The hub in the center corresponds to the precursor invention by Hounsfield [12]. We have detected $m = 5$ different modules in the final CT network (f) using a specific algorithm of community detection (see [13]). Modules are indicated with different shades of gray (see Table for a functional description). We can trace the evolution of modules by shading nodes according to the partition found in (f).Reuse & Permissions
Figure 2
Time evolution of the number of patents $N (t)$ in the USPTO data set from 1973 to 2004. Inset: Cumulative number of patents on a log-log scale, showing a scaling law $N (t) \sim t^{θ}$ with $θ \approx 1.45$ .Reuse & Permissions
Figure 3
(a) In-degree distribution for the patent citation network follows an extended power-law shape, $P_{i} (k) \sim {(k + k_{0})}^{- γ}$ . Three distributions are displayed for three different time windows, namely 1984 (leftmost), 1992 (center), and 2002 (rightmost). (b) The in-degree distribution (filled circles) for the subset of patents displayed in Fig. 1g associated to patents on microchip technology. The corresponding extended scaling fit is also shown (continuous line) using $k_{0} = 6.80 \pm 0.16$ and $γ = 4.73$ .Reuse & Permissions
Figure 4
Hierarchical organization of patent citation networks. Here two networks have been analyzed, corresponding to the 1984 and 1992 data sets. We can clearly appreciate that clustering decays roughly following a power-law behavior (a logarithmic binning has been used). The continuous lines correspond to the theoretical law $C (k) \sim k^{- θ}$ . The estimated exponents are indicated.Reuse & Permissions
Figure 5
(a) Illustration of the kernel estimation procedure. We compare two consecutive patent network snapshots indicated by all patents existing at time $T_{0}$ and the patents created in $[T_{1}, T_{1} + Δ N]$ . Here, $T_{1} > T_{0}$ in order to avoid unwanted biases in the measurements [31]. The probability to cite the $s$ th patent is a function of its age $τ_{s} = T_{0} - s$ and in-degree $k_{s}$ , with $s < T_{0}$ . Patent attachment probability $Π (k, τ)$ is approximated by the fraction of $T_{0}$ citations in the $T_{1}$ network (see text for details). (b) The empirical attachment kernel when $T_{0}$ corresponds to the year 2002 and $T_{1}$ corresponds to the year 2003.Reuse & Permissions
Figure 6
Estimation of the attachment rule for the patent citation network at $T_{1} = 2002$ . (a) The preferential attachment function fits a scaling law $g_{>} (k) \sim k^{β + 1}$ with $β \approx 1$ . Each curve corresponds to nodes having the same age ( $τ = 120$ for the open circles, $τ = 75$ for the filled triangles, and $τ = 50$ for the open squares). (b) Fitting for the aging function $f (τ)$ predicts the Weibull distribution described in the text with $α \approx 1.45$ . Each curve corresponds to nodes having the same in-degree ( $k = 1$ for open circles and $k = 5$ for filled circles). For every curve we have used $T_{1} = T_{0} + 1$ . These curves are cross sections of the attachment kernel [see Fig. 5b].Reuse & Permissions

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