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How Placing Limitations on the Size of Personal Networks Changes the Structural Properties of Complex Networks

Author

Listed:
  • Somayeh Koohborfardhaghighi

    () (College of Engineering, Seoul National University)

  • Jorn Altmann

    () (College of Engineering, Seoul National University)

Abstract

People-to-people interactions in the real world and in virtual environments (e.g., Facebook) can be represented through complex networks. Changes of the structural properties of these complex networks are caused through a variety of dynamic processes. While accepting the fact that variability in individual patterns of behavior (i.e., establishment of random or FOAF-type potential links) in social environments might lead to an increase or decrease in the structural properties of a complex network, in this paper, we focus on another factor that may contribute to such changes, namely the size of personal networks. Any personal network comes with the cost of maintaining individual connections. Despite the fact that technology has shrunk our world, there is also a limit to how many close friends one can keep and count on. It is a relatively small number. In this paper, we develop a multi-agent based model to capture, compare, and explain the structural changes within a growing social network (e.g., expanding the social relations beyond one's social circles). We aim to show that, in addition to various dynamic processes of human interactions, limitations on the size of personal networks can also lead to changes in the structural properties of networks (i.e., the average shortest-path length). Our simulation result shows that the famous small world theory of interconnectivity holds true or even can be shrunk, if people manage to utilize all their existing connections to reach other parties. In addition to this, it can clearly be observed that the network¡¯s average path length has a significantly smaller value, if the size of personal networks is set to larger values in our network growth model. Therefore, limitations on the size of personal networks in network growth models lead to an increase in the network¡¯s average path length.

Suggested Citation

  • Somayeh Koohborfardhaghighi & Jorn Altmann, 2014. "How Placing Limitations on the Size of Personal Networks Changes the Structural Properties of Complex Networks," TEMEP Discussion Papers 2014110, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Jan 2014.
  • Handle: RePEc:snv:dp2009:2014110
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    File URL: ftp://147.46.237.98/DP-110.pdf
    File Function: First version, 2014
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    Cited by:

    1. Somayeh Koohborfardhaghighi & Jorn Altmann, 2014. "How Variability in Individual Patterns of Behavior Changes the Structural Properties of Networks," TEMEP Discussion Papers 2014114, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Jun 2014.
    2. Somayeh Koohborfardhaghighi & Jorn Altmann, 2014. "A Network Formation Model for Social Object Networks," TEMEP Discussion Papers 2014113, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Jun 2014.
    3. Somayeh Koohborfardhaghighi & Jorn Altmann, 2014. "How Structural Changes in Complex Networks Impact Organizational Learning Performance," TEMEP Discussion Papers 2014111, Seoul National University; Technology Management, Economics, and Policy Program (TEMEP), revised Mar 2014.

    More about this item

    Keywords

    Small-World Network; Complex Networks; Average Shortest Path Length; Size of Personal Networks; Network Growth Model.;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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