Michael Zaiser * Theory of complex networks (was: [ox-en] Conference documentation / Konferenzdokumentation)
- From: Stefan Merten <smerten oekonux.de>
- Date: Fri, 18 Jan 2008 19:11:15 +0100
Theory of complex networks
Michael Zaiser [M.Zaiser at ed.ac.uk]
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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
o Formally: number of nodes with rank k: N(k) ~ K[-y]
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(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
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o Left: classical
o Right: scale-free
What is exciting about scale-free networks?
o Small-world properties
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 oekonux.de