On algebraic graph theory and the dynamics of innovation networks
Abstract
We investigate some of the properties and extensions of a dynamic
innovation network model recently introduced in [37]. In the model, the set
of efficient graphs ranges, depending on the cost for maintaining a link, from
the complete graph to the (quasi-) star, varying within a well defined class of
graphs. However, the interplay between dynamics on the nodes and topology
of the network leads to equilibrium networks which are typically not efficient
and are characterized, as observed in empirical studies of R&D networks, by
sparseness, presence of clusters and heterogeneity of degree. In this paper,
we analyze the relation between the growth rate of the knowledge stock of the
agents from R&D collaborations and the properties of the adjacency matrix associated
with the network of collaborations. By means of computer simulations
we further investigate how the equilibrium network is affected by increasing the
evaluation time τ over which agents evaluate whether to maintain a link or not.
We show that only if τ is long enough, efficient networks can be obtained by
the selfish link formation process of agents, otherwise the equilibrium network
is inefficient. This work should assist in building a theoretical framework of
R&D networks from which policies can be derived that aim at fostering efficient
innovation networks.