Qual Quant (2015) 49:1559–1571
Diffusion of innovations in dense and sparse networks
Published online: 31 July 2014
© Springer Science+Business Media Dordrecht 2014
Abstract This paper puts forward a comparison of the performance of sparsely and densely
connected social networks in promoting the diffusion of innovations of uncertain proﬁtability.
To this end, we use a threshold model of innovation diffusion, based on a classic model
of adoption of innovations via imitation by Jensen (Int. J. Ind. Organ. 6:335–350, 1988),
to evaluate the probability of diffusion of an innovation in three classes of networks: the
circular, the star-shaped and the complete networks. We ﬁnd that, if agents hold a low prior
conﬁdence in the proﬁtability of an innovation, then complete networks and star networks
with informed agents (i.e., with agents who are aware of the structure of the network and use
this information rationally) perform better than circles and than stars with myopic agents.
The converse is true for innovations accompanied by initial high expectations about their
Keywords Innovation diffusion · Propagation in networks · Imitative behaviour
There is large evidence and consensus about the fact that the diffusion of an innovation is a
social process, in as much as it unfolds across networks of agents who are somehow connected
to one another, and that the choice of action of the individuals is inﬂuenced by choices made
by other agents in the network.
There is also large consensus among the scholars about the
fact that the shape of the social network has important effects on the diffusion process that
takes place in it, but the precise nature of such effects is not clear yet.
Several scholars have investigated this issue using linear threshold models of diffusion,
either running them in numerical simulations (on deterministic or randomly generated net-
In threshold models of diffusion in networks, the structure of the network is represented by its adjacency
matrix, which is utilised to compute recursively the contagion process started by an initial set of adoptions.
M. Eboli (
Dipartimento di Economia Aziendale, Università ‘G. d’Annunzio’, Pescara, Italy