Rob Stocker, David Cornforth and T. R. J. Bossomaier (2002)
Network Structures and Agreement in Social Network Simulations
Journal of Artificial Societies and Social Simulation
vol. 5, no. 4
To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary
<http://jasss.soc.surrey.ac.uk/5/4/3.html>
Received: 31-Jul-2002 Accepted: 28-Sep-2002 Published: 31-Oct-2002
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Figure 1. Representation of network structures: (a) random, (b) scale-free and, (c) hierarchical (Stocker et al. 2001) |
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Figure 2. Patterns of connections to each node in the constrained hierarchical network structure, number of layers = 3, number of nodes in first layer = 1, connections to second layer = 4 and connections to the final layer = 24. This is designated Hierarchy 3λ1λ4λ24. |
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Figure 3. Connectivity pattern for values Z = 0.38 and λ = 1.00. Node 1 has 35 connections and node 5 has 6 connections, the majority of nodes have only 1 or 2 connections. |
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Figure 4. Connectivity pattern for values Z = 0.9999 and λ = 1.71. Node 1 has 14 connections and node 5 has 5 connections, the majority of nodes have only 1 or 2 connections. |
// initialise each node for each node set opinion 0 or 1 set influence between 0 and 1 set susceptibility between 0 and 1 next node // initialise node connectivity for hierarchy OR scale-free if hierarchy for each node i in current layer select different node j in next layer create link between i and j next node i if scale-free for each node i k = number of connections for node i for each node j from 1 to k create link between i and j next node j next node i // execute interaction between connected nodes for time step (1000) for node i (1 to population) for node j (1 to population) if node i connected to node j if influence of node (i > j) AND susceptibility of node (i < j) state of j = state of i else if influence of node (i < j) AND susceptibility of node (i > j) state of i = state of j next node j next node i record state of each node for each time step next time step
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Figure 5. Agreement patterns through time for the random general tree hierarchical network structure, demonstrating stability through all time steps |
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Figure 6. The percentage of nodes that changed state settling to stability through 0 to 100 time steps, indicating a possible chaotic attractor |
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Figure 7. Representative of the consistent and stable patterns of opinions in hierarchical structures, this system comprised six layers with one node in the top layer. For subsequent layers, there are two links from the previous layer and four links to the final layer resulting in a population of 95 for this structure |
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Figure 8. Relatively narrow3-layer hierarchical structure with 2 nodes in the top layer, 6 links to the second layer and 7 links to the final layer, demonstrates stable opinion patterns (compare Fig 7) suggesting a point of attraction |
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Figure 9. For this 4-layer structure, the number of links from the first layer to the second exceeds the number of links to subsequent layers. Note the stable patterns of opinion. |
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Figure 10. Representative of broad hierarchical structures, this 2-layer hierarchical network with one node in the top layer and links to ninety-nine nodes in the lowest layer, demonstrates complex behaviour and instability over time, where opinion patterns fluctuate from 20 per cent to 50 per cent. |
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Figure 11. Scale-free network with Z = 0.38, λ = 1.00 showing significant change in number of "yes" around 100 time steps. |
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Figure 12. Scale-free network with Z = 0.38, λ = 1.00 showing corresponding the protuberance or increase in the number of nodes changing state at around 100 time steps |
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Figure 13. Scale-free network with Z = 0.9999, λ = 1.71 showing gradual move to stable opinion patterns over the first 100 time steps |
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Figure 14. Scale-free network with Z = 0.9999, λ = 1.71 showing an increase in the number of nodes changing state at around 100 time steps that is similar to Z = 0.38, λ = 1.00. |
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