American Institute of Mathematical Sciences

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

On algebraic graph theory and the dynamics of innovation networks

M. D. König 1, , Stefano Battiston 2, , M. Napoletano 1, and  F. Schweitzer 1,

1. 

Chair of Systems Design, ETH Zürich, Kreuzplatz 5, CH-8032 Zürich, Switzerland, Switzerland, Switzerland
2. 

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.
Keywords: Innovation Networks, Algebraic Graph Theory, Network Formation.
Mathematics Subject Classification: 37N40, 05C5.
Citation: M. D. König, Stefano Battiston, M. Napoletano, F. Schweitzer. On algebraic graph theory and the dynamics of innovation networks. Networks and Heterogeneous Media, 2008, 3 (2) : 201-219. doi: 10.3934/nhm.2008.3.201
[1]

Mirela Domijan, Markus Kirkilionis. Graph theory and qualitative analysis of reaction networks. Networks and Heterogeneous Media, 2008, 3 (2) : 295-322. doi: 10.3934/nhm.2008.3.295
[2]

Konstantin Avrachenkov, Giovanni Neglia, Vikas Vikram Singh. Network formation games with teams. Journal of Dynamics and Games, 2016, 3 (4) : 303-318. doi: 10.3934/jdg.2016016
[3]

Milo Viviani. An algebraic approach to the spontaneous formation of spherical jets. Journal of Computational Dynamics, 2022, 9 (2) : 279-298. doi: 10.3934/jcd.2021028
[4]

Liu Hui, Lin Zhi, Waqas Ahmad. Network(graph) data research in the coordinate system. Mathematical Foundations of Computing, 2018, 1 (1) : 1-10. doi: 10.3934/mfc.2018001
[5]

Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279
[6]

Barton E. Lee. Consensus and voting on large graphs: An application of graph limit theory. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1719-1744. doi: 10.3934/dcds.2018071
[7]

Peter Hinow, Edward A. Rietman, Sara Ibrahim Omar, Jack A. Tuszyński. Algebraic and topological indices of molecular pathway networks in human cancers. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1289-1302. doi: 10.3934/mbe.2015.12.1289
[8]

Yvjing Yang, Yang Liu, Jungang Lou, Zhen Wang. Observability of switched Boolean control networks using algebraic forms. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1519-1533. doi: 10.3934/dcdss.2020373
[9]

V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks and Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621
[10]

Yao-Li Chuang, Tom Chou, Maria R. D'Orsogna. A network model of immigration: Enclave formation vs. cultural integration. Networks and Heterogeneous Media, 2019, 14 (1) : 53-77. doi: 10.3934/nhm.2019004
[11]

Marco Scianna, Luca Munaron. Multiscale model of tumor-derived capillary-like network formation. Networks and Heterogeneous Media, 2011, 6 (4) : 597-624. doi: 10.3934/nhm.2011.6.597
[12]

Leon Petrosyan, David Yeung. Shapley value for differential network games: Theory and application. Journal of Dynamics and Games, 2021, 8 (2) : 151-166. doi: 10.3934/jdg.2020021
[13]

Robert Carlson. Spectral theory for nonconservative transmission line networks. Networks and Heterogeneous Media, 2011, 6 (2) : 257-277. doi: 10.3934/nhm.2011.6.257
[14]

Maya Mincheva, Gheorghe Craciun. Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks. Mathematical Biosciences & Engineering, 2013, 10 (4) : 1207-1226. doi: 10.3934/mbe.2013.10.1207
[15]

A. C. Eberhard, J-P. Crouzeix. Existence of closed graph, maximal, cyclic pseudo-monotone relations and revealed preference theory. Journal of Industrial and Management Optimization, 2007, 3 (2) : 233-255. doi: 10.3934/jimo.2007.3.233
[16]

Xianmin Geng, Shengli Zhou, Jiashan Tang, Cong Yang. A sufficient condition for classified networks to possess complex network features. Networks and Heterogeneous Media, 2012, 7 (1) : 59-69. doi: 10.3934/nhm.2012.7.59
[17]

Jacek Banasiak, Adam Błoch. Telegraph systems on networks and port-Hamiltonians. Ⅱ. Network realizability. Networks and Heterogeneous Media, 2022, 17 (1) : 73-99. doi: 10.3934/nhm.2021024
[18]

Jian-Jun Xu, Junichiro Shimizu. Asymptotic theory for disc-like crystal growth (II): interfacial instability and pattern formation at early stage of growth. Communications on Pure and Applied Analysis, 2004, 3 (3) : 527-543. doi: 10.3934/cpaa.2004.3.527
[19]

Ross Cressman, Vlastimil Křivan. Using chemical reaction network theory to show stability of distributional dynamics in game theory. Journal of Dynamics and Games, 2021  doi: 10.3934/jdg.2021030
[20]

Serap Ergün, Bariş Bülent Kırlar, Sırma Zeynep Alparslan Gök, Gerhard-Wilhelm Weber. An application of crypto cloud computing in social networks by cooperative game theory. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1927-1941. doi: 10.3934/jimo.2019036

2021 Impact Factor: 1.41

Tools

Metrics

  • PDF downloads (573)
  • HTML views (0)
  • Cited by (23)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy