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Michael Zaiser * Theory of complex networks (was: [ox-en] Conference documentation / Konferenzdokumentation)

Theory of complex networks

Michael Zaiser [M.Zaiser at]

** Unable to import figure Zaiser1.png **


Why / when does this e-mail protocol work?

1.   If this message is for you, read it. Stop.

2.   If you know the recipient, give him this card. Stop.

3.   If you don't know the recipient, give this card to someone else.

o    If you hand it to someone in the street at random: No

o    If you hand it to someone you know: Possibly

o    If you hand it to someone in a collaboration network(say,
     Oekonux): Probably yes

Such protocols work for communication within networks of a certain
structure. What is this structure?

Some Definitions on Networks

o    Consist of NODES and EDGES (Links)

o    Edges may be DIRECTED or UNDIRECTED

o    Social networks: Nodes are individuals or groups of individuals

o    Links may be collaborations, acts of communication, acts of


o    Networks with directed links

     o    World-Wide Web

     o    Network of long-distance calls

o    Networks with undirected links

     o    Internet (Router level)

     o    Social Acquaintances

How to characterize a Network?

o    Qualitatively: Graphs

o    Quantitatively: Ranks + Correlations

     o    Rank = number of links connecting to/from a node

     o    Correlations = Properties of adjacent nodes (mixing,

     A network for which a 'characteristic rank' cannot be defined is
     called scale-free

o    Formally: number of nodes with rank k: N(k) ~ K[-y]

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Degree Distributions

1.   Scale-free

     (WWW, In-degree)

2.   Classical

     (US power grid)

o    Social examples of scale-free networks:

     o    Scientific collaborations (Physics)

     o    E-mail exchanges

     o    Long-distance calls

o    Non-scale free networks

     o    Acquaintance

     o    Friendship

** Unable to import figure Zaiser3.png **

o    Left: classical

o    Right: scale-free

What is exciting about scale-free networks?

o    Small-world properties

o    Resilience

o    Bandwidth requirements

o    'Non-standard' data transmission properties:

     o    Tendency to overload hubs

     o    Efficiency of non-standard transmission protocols (rumour
          spreading, viral spreading)

o    Form by self-organization processes

Other properties in real social SON:

o    Clustering, combination of local and global collaborations


o    no limits to link formation

o    free association

o    growing networks

o    preferential attachment


o    earth-bound networks

o    aging (old-boys networks)


o    Self-organized networks as tools/machines for information

o    Scale-free social networks are made possible by technology, but
     their functioning is not a technological issue.

o    These networks are not non-hierarchical.

o    Hierarchy in such networks is not primarily a problem of personal
     virtue ('taking responsibility') or personal misconduct.

o    Hierarchy emerging from self-organization reflects functionality
     and is inherently transient.

Contact: projekt

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