created with NetLogo
The model is an example of a simplified dynamic social network of acquaintanceships. It was developed as a stylized real-world model for the framework of probabilistic inductive classes of graphs (see references).
The model considers one graph as a basis (200 randomly connected persons with 200 links) and two rules: (1) breaking up of an acquaintanceship for a more "adantageous" one and (2) creation of "stronger" relationships by forming connected triads.
In each time step, one of the rules is applied according to a prespecified probability distribution.
The model starts with 200 nodes randomly connected with 200 links.
At each step, one of the rules is selected: (1) a link is selected and one end of it is randomly rewired or (2) a path of 4 is selected and from it a triangle is created, leaving the last/first node disconnected.
Selection of the existing nodes is random (keeping in mind, that the graph has to stay simple).
Buttons:
SETUP --- sets the base (200 randomly connected nodes)
GO ONCE --- makes one step (chooses the rule and applies it)
GO --- continuously builds steps until pressing the button again
REDO LAYOUT --- redoes the layout according to Fruchterman-Reingold spring embedder
RESIZE NODES --- the size of the node corresponds to its degree
Slider:
PROBABILITY --- selecting a probability of choosing rule 1
Switches:
LAYOUT? --- controls whether or not the layout procedure is run; the procedure attempts to move the nodes around to make the structure of the network easier to see
PLOT? --- turns off the plots which speeds up the model
COLOR? --- turns on/off colors for nodes
If you want the model to run faster, you can turn off the LAYOUT? and PLOT? switches and/or freeze the view (using the on/off button in the control strip over the view). The LAYOUT? switch has the greatest effect on the speed of the model.
If you have LAYOUT? switched off, and then want the network to have a more appealing layout, press the REDO LAYOUT button which will run the layout-step procedure until you press the button again. You can press REDO LAYOUT at any time even if you had LAYOUT? switched on and it will try to make the network easier to see.
Color enabled:
When rule 1 is selected, the selected 2 nodes, that connect appear large green.
When rule 2 is selected, the 3 selected nodesm that form a triangle appear large red.
You can see the degree distribution of the network in this model by looking at the plots. The top plot is a histogram of the degree of each node. The bottom plot shows the same data, but both axes are on a logarithmic scale. When degree distribution follows a power law, it appears as a straight line on the log-log plot. One simple way to think about power laws is that if there is one node with a degree distribution of 1000, then there will be ten nodes with a degree distribution of 100, and 100 nodes with a degree distribution of 10. (Wilensky - see references)
Let the model run a little while. Try also different number of links.
Change the probability of a model to a very small value (mostly triangles are going to be formed).
(less links, low probability for rule 1, network might exibit separation to more connected components - here we disregard isolated points as components)
Both nodes and edges are turtles. Edge turtles have the "line" shape. The edge turtle's SIZE variable is used to make the edge be the right length.
Lists are used heavily in this model. Each node maintains a list of its neighboring nodes.
This model is based on:
N. Kejzar, Z. Nikoloski and V. Batagelj: Probabilistic Inductive Classes of Graphs, arXiv:math/0612778v1 [math.DS], 2007.
The layout algorithm is based on the Fruchterman-Reingold layout algorithm. More information about this algorithm can be obtained at: http://citeseer.ist.psu.edu/fruchterman91graph.html.
see also model of Wilensky, U. (2005). NetLogo Preferential Attachment model. http://ccl.northwestern.edu/netlogo/models/PreferentialAttachment. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.