Connections
While agents often interact with strangers, interactions with familiars-- friends, relatives, partners, enemies—are more common.
We commonly represent the relationship between two familiars as a link or arrow between two nodes (i.e., agents):
A simple social network can then be represented as a graph of agents and connections:
If links in a graph represent friendships, for example, then the popularity of an agent is the ratio of the number of links to other agents (i.e., number of friendships) with the number of possible friendships. For example, the popularity of a1 above is 1/3.
A cluster is a sub-network in which all agents are linked to each other directly or indirectly. For example, if a5 and a6 in the above network weren't friends, then there would be two clusters.
The clustering coefficient (cc) of a network is the percentage of pairs of agents that are linked. The cc of the network above is 12/55.
The average path length (apl) of a network/cluster is the average number of links that connect any two agents. The apl of the example above is 2.52:
|
agent |
a0 |
a1 |
a2 |
a3 |
a4 |
a5 |
a6 |
a7 |
a8 |
a9 |
average |
|
a0 |
0 |
1 |
5 |
6 |
6 |
4 |
3 |
3 |
2 |
2 |
3.20 |
|
a1 |
1 |
0 |
4 |
5 |
5 |
3 |
2 |
2 |
1 |
1 |
2.40 |
|
a2 |
5 |
4 |
0 |
1 |
1 |
1 |
2 |
3 |
4 |
4 |
2.50 |
|
a3 |
6 |
5 |
1 |
0 |
1 |
2 |
3 |
4 |
4 |
5 |
3.10 |
|
a4 |
6 |
5 |
1 |
1 |
0 |
2 |
3 |
4 |
4 |
5 |
3.10 |
|
a5 |
4 |
3 |
1 |
2 |
2 |
0 |
1 |
2 |
2 |
3 |
2.00 |
|
a6 |
3 |
2 |
2 |
3 |
3 |
1 |
0 |
1 |
2 |
3 |
2.00 |
|
a7 |
3 |
2 |
3 |
4 |
4 |
2 |
1 |
0 |
1 |
2 |
2.20 |
|
a8 |
2 |
1 |
4 |
4 |
4 |
2 |
2 |
1 |
0 |
1 |
2.10 |
|
a9 |
2 |
1 |
4 |
5 |
5 |
3 |
3 |
2 |
1 |
0 |
2.60 |
|
|
|
|
|
|
|
|
|
|
|
|
2.52 |
Networks with short average path lengths and high clustering coefficients are called small world networks.
Bridges
Social networks tend to form homophilic clusters-- clusters in which the agents share traits such as class, status, race, etc.
A bridge is a link that joins two clusters. The connection between a5 and a6 in the example above is a bridge.
Scale Free Networks
A network is scale free if the popularity distribution
follows the inverse power law:
Popular agents are called hubs. Scale-free networks tend to be robust: paths can be reestablished if an agent is removed, unless the agent is a hub, but they are rare.
Like the Internet, social networks tend to be small world scale free networks.
NetLogo Models
We have seen that turtles and patches are two types of agents in a NetLogo model. Links are a third type. A link connects two turtles. A link can be directed or undirected.
Links can be created and killed, they can own properties and be divided into breeds, but unlike turtles and patches, they don't have positions.
Examples
Preferential Attachment
Team Assembly