June  2008, 3(2): 201-219. doi: 10.3934/nhm.2008.3.201

On algebraic graph theory and the dynamics of innovation networks


Chair of Systems Design, ETH Zürich, Kreuzplatz 5, CH-8032 Zürich, Switzerland, Switzerland, Switzerland


Chair of Systems Design, ETH Zürich, Kreuzplatz 5, 8032 Zürich

Received  November 2007 Revised  February 2008 Published  March 2008

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 as- sociated with the network of collaborations. By means of computer simulations we further investigate how the equilibrium network is affected by increasing the evaluation time $\tau$ over which agents evaluate whether to maintain a link or not. We show that only if $\tau$ 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.
Citation: M. D. König, Stefano Battiston, M. Napoletano, F. Schweitzer. On algebraic graph theory and the dynamics of innovation networks. Networks & Heterogeneous Media, 2008, 3 (2) : 201-219. doi: 10.3934/nhm.2008.3.201

Ville Salo, Ilkka Törmä. Recoding Lie algebraic subshifts. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 1005-1021. doi: 10.3934/dcds.2020307


Qiang Fu, Yanlong Zhang, Yushu Zhu, Ting Li. Network centralities, demographic disparities, and voluntary participation. Mathematical Foundations of Computing, 2020, 3 (4) : 249-262. doi: 10.3934/mfc.2020011


D. R. Michiel Renger, Johannes Zimmer. Orthogonality of fluxes in general nonlinear reaction networks. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 205-217. doi: 10.3934/dcdss.2020346


Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344


Shipra Singh, Aviv Gibali, Xiaolong Qin. Cooperation in traffic network problems via evolutionary split variational inequalities. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020170


Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020451


H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020433


Pierre-Etienne Druet. A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020458


Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2020051


Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024


Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276

2019 Impact Factor: 1.053


  • PDF downloads (250)
  • HTML views (0)
  • Cited by (7)

[Back to Top]