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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. Stop.

• If you hand it to someone in the street at random: No
• If you hand it to someone you know: Possibly
• 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

• Consist of NODES and EDGES (Links)
• Edges may be DIRECTED or UNDIRECTED
• Social networks: Nodes are individuals or groups of individuals
• Links may be collaborations, acts of communication, acts of exchange

Examples

• Networks with directed links
  • World-Wide Web
  • Network of long-distance calls
• Networks with undirected links
  • Internet (Router level)
  • Social Acquaintances

How to characterize a Network?

• Qualitatively: Graphs
• Quantitatively: Ranks + Correlations
  • Rank = number of links connecting to/from a node
  • Correlations = Properties of adjacent nodes (mixing, clustering)
  
  A network for which a 'characteristic rank' cannot be defined is called scale-free
• Formally: number of nodes with rank k: N(k) ~ K^-y

Degree Distributions

1. Scale-free
   (WWW, In-degree)
2. Classical
   (US power grid)

• Social examples of scale-free networks:
  • Scientific collaborations (Physics)
  • E-mail exchanges
  • Long-distance calls
• Non-scale free networks
  • Acquaintance
  • Friendship

• Left: classical
• Right: scale-free

What is exciting about scale-free networks?

• Small-world properties
• Resilience
• Bandwidth requirements
• 'Non-standard' data transmission properties:
  • Tendency to overload hubs
  • Efficiency of non-standard transmission protocols (rumour spreading, viral spreading)
• Form by self-organization processes

Other properties in real social SON:

• Clustering, combination of local and global collaborations

Conditions

• no limits to link formation
• free association
• growing networks
• preferential attachment

Obstacles

• earth-bound networks
• aging (old-boys networks)

Issues/Theses

• Self-organized networks as tools/machines for information exchange/collaboration/production.
• Scale-free social networks are made possible by technology, but their functioning is not a technological issue.
• These networks are not non-hierarchical.
• Hierarchy in such networks is not primarily a problem of personal virtue ('taking responsibility') or personal misconduct.
• Hierarchy emerging from self-organization reflects functionality and is inherently transient.