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Coexistence in Preferential Attachment Networks

Part of: Combinatorial probability Stochastic processes Graph theory

Published online by Cambridge University Press:  09 February 2016

TONĆI ANTUNOVIĆ ,
ELCHANAN MOSSEL  and
MIKLÓS Z. RÁCZ
TONĆI ANTUNOVIĆ
Affiliation:
University of California, Los Angeles, CA 90025, USA (e-mail: tantunovic@math.ucla.edu)
ELCHANAN MOSSEL
Affiliation:
The Wharton School of the University of Pennsylvania, Philadelphia, PA 19104, USA and University of California, Berkeley, CA 94720, USA (e-mail: mossel@wharton.upenn.edu)
MIKLÓS Z. RÁCZ
Affiliation:
University of California, Berkeley, CA 94720, USA (e-mail: racz@stat.berkeley.edu)
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Abstract

We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses neighbours by preferential attachment, and selects its type based on the number of initial neighbours of each type. The model is analysed in detail, and in particular, we determine the possible proportions of the various types in the limit of large networks. An important qualitative feature we find is that, in contrast to many current theoretical models, often several competitors will coexist. This matches empirical observations in many real-world networks.

MSC classification

Primary: 05C80: Random graphs
Secondary: 60C05: Combinatorial probability 60G99: None of the above, but in this section
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 6 , November 2016 , pp. 797 - 822
Copyright
Copyright © Cambridge University Press 2016 

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