Page 184 - JOURNAL OF LIBRARY SCIENCE IN CHINA 2015 Vol. 41

Ge SONG / The diffusion process of academic innovation 183

obtain the lowest cutoff value that yields a component that connects at least one source vertex to
another sink vertex, the cutoff value is usually equal to the lowest traversal weight on the main
paths.

1.3 Basis indices

The indices such as breadth, speed, strength and delay, etc. can describe the basic features of
innovation diffusion. According to diffusion theory, social network analysis and citation analysis,
the definitions and calculation formulas of the corresponding indices have been put forward as
follows:
1) Diffusion rate (dr): In diffusion theory, the rate of diffusion can be measured by the adoption
rate, which is the number of new adopters appearing at a particular moment. The calculation
formula is as follows:

dr t =ca t -ca t-1
Among them, dr t is the diffusion rate at time t, ca t is the cumulative adopters at time t.
2) Diffusion acceleration (da): the amount of change happens to the diffusion rate at a certain
time. The calculation formula is as follows:

da t =dr t -dr t-1
Among them, da t is the diffusion acceleration at time t.
3) Diffusion breadth (db): the number of research areas adopted an innovation.
4) Diffusion strength (ds): the flow of innovative knowledge trafficking from one research area
to another which can be measured by the number of citations from the latter to the former. So
diffusion strength is a vector.
5) Diffusion delay (dd): the time span between the adoption time of a research area adopting an
innovation and the occurrence time of the innovation in primary field. The calculation formula is
as follows:
dd=t a -t o
Among them, t a is the adoption time of a research area, while t o is the occurrence time of an
innovation.

2 Data sources

Ronald Burt put forwards the famous concept of structural holes in his book Structural holes: The
social structure of competition in 1992. Currently, structural holes theory has been widely applied
in the Social Sciences, and its related research has been very active. Therefore, taking structural
holes as an example has typical representativeness for the study of diffusion process of academic
innovation.