Network theory

Presented at Blah emerging church conference 21.07.06

1. Social networks:

  • Smaller, tighter networks can be less useful to their members than networks with lots of loose connections (weak ties) to individuals outside the main network.
  • More "open" networks, with many weak ties and social connections, are more likely to introduce new ideas and opportunities to their members than closed networks with many redundant ties.
  • It is better for individual success to have connections to a variety of networks rather than many connections within a single network.

2. The rule of 150:

  • The so-called rule of 150, states that the size of a genuine social network is limited to about 150 members [sometimes called Dunbar's number or the monkeysphere]
  • It is theorized in evolutionary psychology that the number may be some kind of limit of average human ability to recognize members and track emotional facts about all members of a group.
  • However, it may be due to economics and the need to track "free riders", as larger groups tend to more freely allow cheats and liars to prosper.

3. Opinion leaders & change agents:

  • The opinion leader is the agent who is an active media user and who interprets the meaning of media messages or content for lower-end media users.
  • Opinion leadership tends to be subject specific, that is, a person that is an opinion leader in one field may be a follower in another field.
  • A change agent or agent of change is someone who engages either deliberately or whose behavior results in social, cultural or behavioral change.

4. Small world phenomenon 1:

  • "Collective dynamics of 'small-world' networks" Nature magazine June 1998 by Duncan J. Watts and Steven H. Strogatz, both in the Department of Theoretical and Applied Mechanics at Cornell University
  • First mathematical model of the small-world phenomenon in networks
  • Watts and Strogatz showed that, beginning with a regular lattice, the addition of a small number of random links reduces the diameter - the longest direct path between any two vertices in the network - from being very long to being very short.
  • The research was originally inspired by Watts' efforts to understand the synchronization of cricket chirps, which show a high degree of coordination over long ranges as though the insects are being guided by an invisible conductor.

5. Small world phenomenon 2:

  • Regular lattice:
    nodes connect to all the nodes near to them [clustering]
    average path length high because it takes many steps to get across the lattice [the train that stops at every stop]
  • Random lattice:
    nodes connect near and far at random
    average path length low but little local connectivity [loss of clusters]
  • Small-world lattice:
    as soon as one or two nodes link at random across the lattice the path-length drops dramatically while retaining high clustering
  • ie the loss of local [cluster] connectivity caused by one member dropping a cluster connection for an external or hub connection is small compared to the leap in connectivity caused by the onset of small-world
  • "the transition to a small world [by one edge moving from local to trans-network] is almost undetectable at the local level."

6. Preferential attachment:

  • Networks expand continuously by the addition of new vertices, and new vertices attach preferentially to already well connected sites.
  • Preferential attachment:
    new nodes connect to other nodes in proportion to the number of connections those nodes already possess
    a node that has more connections will increase its connectivity at a higher rate
    so an initial difference in connectivity will increase as the network grows
    older vertices increase their connectivity at the expense of the younger ones
    also known as a rich-get-richer model
  • the highly connected nodes become hubs through which a high proportion of small-world paths pass

7. Damage:

  • In a small-world network loss of a random node seldom causes does much damage, because most shortest paths flow through hubs
  • However, if random deletion hits a hub by chance the average path length increases dramatically
  • By contrast, in a random network, in which all nodes have roughly the same number of connections, deleting a random node is likely to increase the mean-shortest path length slightly but significantly for almost any node deleted.
  • In this sense, random networks are vulnerable to random perturbations, whereas small-world networks are robust. However, small-world networks are vulnerable to targeted attack of hubs, whereas random networks cannot be targeted for catastrophic failure.

8. Some implications:

  • It is worth every group having one person whose role is to connect externally even if they are not then contributing as fully to the local cluster
  • If a group has only local external connections its horizon is short - it will feel isolated even if the eventual connectivity is far-flung
  • If a group has one long-distance or hub connection its horizon will be distant
  • 'Always same people at events' phenomenon is to be expected - they are the small-world connectors & hubs
  • Monkeysphere concept suggests a natural limit to a single network or 'scene'
  • Combination of monkeysphere and smallworld suggests that not everybody can be widely connected - your monkeysphere is either used up locally or as a hub


All rights remain with the original sources above except 'Some implications' section by Steve Collins