Measuring and Modeling Complex Networks Across Domains
This project is related to our research line: Financial Networks and R&D Networks
Duration: 40 months (February 2005  May 2008)
Funding source: EU 6th Framework Programme, NEST PATHFINDER: “Tackling complexity in science” (Contract No 12999 NEST)
Project partners: University of Oxford (UK), Technische Universität Dresden (Germany), Politechnika Warszawska (Poland), INSEAD Business School, (France), ETH Zurich (Switzerland), Stockholm University (Sweden)
Official website: MMCOMNET
The MMCOMNET project has set out to measure and model complex networks from different domains, with the goal of understanding their structure, function and behaviour. The project seeks to integrate macroscopic or topdown approaches, and bottomup approaches utilising recent findings from the science of complexity. The investigation focuses on data and models of some specific systems chosen as examples from three different domains, representing biological, socioeconomic and innovation networks. These systems include: fungal networks, textile supply networks, credit networks, venture capital networks, road and transportation networks. The project exploits advances in complexity science to elucidate the individual and collective behaviour of agents. The participants are developing models which simulate the different combinations of agents and network dynamics that can account for desirable behaviour. Criteria for choosing between alternative combinations provide insights into how agents and networks adapt, and the tradeoffs that occur between different network functions. In the case of the supplychain model, for example, the conditions that enable networks to retain their integrity in the face of local disruptions are being investigated.
The overall aim of the project is to generate modelling approaches and formulate universal principles to aid in the management of complex networks in realworld situations. The desirable properties observed in model networks can potentially be transferred to networks involving computers, information, business and enterprise, power grids, and railway or other transport systems. The potential longterm benefits from this project are therefore great, and could improve the quality of life of almost everybody in the EU.
Modeling evolving innovation networks

[2009]

Koenig, Michael D;
Battiston, Stefano;
Schweitzer, Frank

Innovation Networks . New Approaches in Modelling and Analyzing

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Abstract We develop a new framework for modeling innovation networks which evolve over time. The nodes in the network represent firms, whereas the directed links represent unilateral interactions between the firms. Both nodes and links evolve according to their own dynamics and on different time scales. The model assumes that firms produce knowledge based on the knowledge exchange with other firms, which involves both costs and benefits for the participating firms. In order to increase their knowledge production, firms follow different strategies to create and/or to delete links with other firms. Dependent on the information firms take into account for their decision, we find the emergence of different network structures. We analyze the conditions for the existence of these structures within a mathematical approach and underpin our findings by extensive computer simulations which show the evolution of the networks and their equilibrium state. In the discussion of the results, particular attention is given to the emergence of direct and indirect reciprocity in knowledge exchange, which refers to the emergence of cycles in the network structure. In order to motivate our modeling framework, in the first part of the chapter we give a broad overview of existing literature from economics and physics. This shows that our framework bridges and extends two different lines of research, namely the study of equilibrium networks with simple topologies and the dynamic approach of hypercycle models.
From Graph Theory to Models of Economic Networks. A Tutorial

[2009]

Koenig, Michael D;
Battiston, Stefano

Networks, Topology and Dynamics: Theory and Applications to Economics and Social Systems

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Abstract Networks play an important role in a wide range of economic phenomena. Despite this fact, standard economic theory rarely considers economic networks explicitly in its analysis. However, a major innovation in economic theory has been the use of methods stemming from graph theory to describe and study relations between economic agents in networks. This recent development has lead to a fast increase in theoretical research on economic networks. In this tutorial, we introduce the reader to some basic concepts used in a wide range of models of economic networks.
On Algebraic Graph Theory and the Dynamics of Innovation Networks

[2008]

Koenig, Michael D;
Battiston, Stefano;
Napoletano, Mauro;
Schweitzer, Frank

Networks and Heterogeneous Media,
pages: 201219,
volume: 3,
number: 2

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Abstract We investigate some of the properties and extensions of a dynamic innovation network model recently introduced in [Koenig et al. Games and Eco. Beh. 752 p694p713 (2012)]. 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 $ 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.
Trade Credit Networks and systemic risk

[2008]

Battiston, Stefano;
Delli Gatti, Domenico;
Gallegati, Mauro

Understanding Complex Systems,
pages: 219239,
volume: 2008

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Abstract In this chapter, we present a model recently introduced in [14, 16] and we discuss the features of a networked economy in which N firms are organised in M production levels. Each firm at a certain level is supplied by a subset of firms in the upper level (suppliers) and supplies a subset of the firms in the lower level (customers). The bottom level consists of retailers, i.e., firms that sell in the consumer market. The top level consists of firms that provide primary goods to the other firms. Firms are connected by means of two mechanisms: (i) the output of supplier firms is an input for customer firms; (ii) supplier firms extend trade credit to customers (as it is typically the case in reality). However, in the model, the trade credit contract is only implicitly sketched: we neither design the optimal trade credit scheme nor look for the optimal amount of trade credit a customer firm should require. Instead, we focus on the mechanisms of propagation of bankruptcy .
The Network of Interregional Direct Investment Stocks across Europe

[2007]

Battiston, Stefano;
Rodrigues, Joao F.;
Zeytinoglu, Hamza

ACS  Advances in Complex Systems,
pages: 2951,
volume: 10,
number: 1

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Abstract We propose a methodological framework to study the dynamics of interregional investment flow in Europe from a Complex Networks perspective, an approach with recent proven success in many fields including economics. In this work we study the network of investment stocks in Europe at two different levels: first, we compute the inwardoutward investment stocks at the level of firms, based on ownership shares and number of employees; then we estimate the inwardoutward investment stock at the level of regions in Europe, by aggregating the ownership network of firms, based on their headquarter location. Despite the intuitive value of this approach for EU policy making in economic development, to our knowledge there are no similar works in the literature yet. In this paper we focus on statistical distributions and scaling laws of activity, investment stock and connectivity degree both at the level of firms and at the level of regions. In particular we find that investment stock of firms is power law distributed with an exponent very close to the one found for firm activity. On the other hand investment stock and activity of regions turn out to be lognormal distributed. At both levels we find scaling laws relating investment to activity and connectivity. In particular, we find that investment stock scales with connectivity in a similar way as has been previously found for stock market data, calling for further investigations on a possible general scaling law holding true in economical networks.
Emergence and Evolution of Coalitions in BuyerSeller Networks

[2007]

Walter, Frank Edward;
Battiston, Stefano;
Schweitzer, Frank

Emergent Intelligence of Networked Agents

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Abstract We investigate the dynamics of the creation, development, and breakup of social networks formed by coalitions of agents. As an application, we consider coalition formation in a consumer electronic market. In our model, agents have benefits and costs from establishing a social network by participating in a coalition. Buyers benefit in terms of volume discount and better match of their preferences. Sellers benefit in terms of better predictability of sales volumes. The model allows us to investigate the stability and size of the coalitions as well as the performance of the market in terms of utility of the agents. We find that the system exhibits three different dominating regimes: individual purchasing behaviour, i.e., no social network exists among the agents, formation of several heterogenous coalitions, i.e., a number of social networks which are not connected, as well as condensation to a giant coalition, i.e., a social network involving all agents.
Aggregate dynamics in an evolutionary network model

[2007]

Seufert, A. M.;
Schweitzer, Frank

International Journal of Modern Physics C,
pages: 16591674,
volume: 18,
number: 10

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Abstract We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represented by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows an eigendynamics based on catalytic support from other nodes, whereas on a much slower time scale the network evolves through selection and mutation of its nodesagent. In the first part of the paper, we explain the dynamics of the model by means of characteristic snapshots of the network evolution and confirm earlier findings on crashes and recoveries in the network structure. In the second part, we focus on the aggregate behavior of the network dynamics. We show that the disruptions in the network structure are smoothed out, so that the average evolution can be described by a growth regime followed by a saturation regime, without an initial random regime. For the saturation regime, we obtain a logarithmic scaling between the average connectivity per node ls and a parameter m, describing the average incoming connectivity, which is independent of the system size N.
Selforganization applied to dynamic network layout

[2007]

Geipel, Markus Michael

International Journal of Modern Physics C,
pages: 15371549,
volume: 18,
number: 10

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Abstract As networks and their structure have become a major field of research, a strong demand for network visualization has emerged. We address this challenge by formalizing the well established spring layout in terms of dynamic equations. We thus open up the design space for new algorithms. Drawing from the knowledge of systems design, we derive a layout algorithm that remedies several drawbacks of the original spring layout. This new algorithm relies on the balancing of two antagonistic forces. We thus call it $$em arf for "attractive and repulsive forces". It is, as we claim, particularly suited for a dynamic layout of smaller networks ($n < 10^3$). We back this claim with several application examples from on going complex systems research.
