Regensburg 2007 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Statistical physics of complex networks II

DY 6.6: Talk

Monday, March 26, 2007, 15:45–16:00, H3

Emergence of networks from optimizing local interaction — •Michael König, Stefano Battiston, and Frank Schweitzer — Chair of Systems Design, ETH Zurich, Kreuzplatz 5, 8032 Zurich, Switzerland

We model evolving complex networks in which agents select their interactions with other agents on the basis of a local nonlinear utility function and study the resulting global network structure. Agents can increase each others utility as catalytic processes on a directed dynamic network. Two cases are discussed: (i) Agents can either bilaterally increase each others utility (direct reciprocity) or (ii) unilaterally increase the utility of other agents and hope that they will benefit from the support of another agent (indirect reciprocity). Direct reciprocity corresponds to a cycle of order k=2 in the network, while indirect reciprocity corresponds to a cycle of order k > 2. The emergence of an autocatalytic set (ACS) is the driving process of growth and sustainability in our model. An ACS is a subgraph of a network, each of whose nodes has at least one incoming link belonging to the same subgraph. The core of an ACS consists of a closed cycle. We argue that in case (i) the network evolves towards a random graph consisting of bilateral links, while in case (ii) an ACS will only form if agents percive an extra profit from being part of a directed cycle.