Lynne Hamill and Nigel Gilbert (2009)
Social Circles: A Simple Structure for Agent-Based Social Network Models
Journal of Artificial Societies and Social Simulation
vol. 12, no. 2 3
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Received: 20-Nov-2008 Accepted: 03-Mar-2009 Published: 31-Mar-2009
|Box 1: Network jargon used in this paper|
A network is comprised of nodes and links, which combine to create paths.
The basic characteristics of a node are its degree and clustering coefficient:
The basic characteristics of a network are size, path length and density:
|Compared to a Poisson distribution with the same mean (thin line)||Cumulative, fitted to a power distribution (thin line)|
|Figure 1. Fischer's distribution of personal networks|
|(a) Regular lattice: each node is linked to its four immediate neighbours||(b) Random network: most nodes have three or four links.|
|(c) Small world network: most nodes are linked only to their immediate neighbours.||(d) Preferential attachment (scale-free) network: a few nodes have many links.|
|Figure 2. Examples of four basic models of networks: all with 30 nodes|
despite the random placement of links…most nodes will have approximately the same number of links..Indeed, in a random network, the nodes follow a Poisson distribution with a bell shape and it is extremely rare to find nodes that have a significantly more or fewer links than the average.Not surprisingly, the assortativity index of a random graph can be shown analytically to be zero (Newman 2002). Although such models display the short paths of social networks (Dorogovtsev & Mendes 2003: 105), it is hardly surprising that random networks fail to replicate other key features of social networks because we know that social networks are not in general created by making random links, although Aiello et al's (2001) recent analysis of phone call data suggested that, at the very large scale, random patterns may appear. So random networks are not good models of social networks either.
|Table 1: Summary of characteristics of the four basic network models|
|Personal network size limited||√||√||√||×|
|Variation in size of personal network||×||Limited||Limited||√|
|Short path lengths||×||√||√||×|
|(a) No reciprocity: different social reaches: A knows B but B does not know A||(b) Reciprocity with the same social reach|
|Figure 3. Reciprocity and social reach|
|Figure 4. Degree of connectivity by social reach (sr)|
|Social reach = 15||Social reach = 30|
|Figure 5. Examples of how networks vary with the size of the social reach. (Red nodes, grey links.)|
|Box 2: Mathematics of circles|
|Figure 6. Cluster coefficient for the single-reach model with the social reach (sr) set at 15, 30 and 50|
|Box 3: Calculating the cluster coefficient: example and pseudo-code|
|Figure 7. Assortativity of degree: typical example of correlation between degrees of connectivity: social reach of 30|
|If E is a Green, then E links with everyone in the smaller (green) circle. If E is a Blue, then E also links to the three Blues within the larger (blue) circle||A link between Blues B1 and B2 creates a short-cut and, for Blues, reduces clustering. The shaded area indicates overlap between the Blues' circles.|
|Figure 8. Two-reach model|
|Figure 9. Examples of two-reach models: Blues 25 percent. (PN = personal network)|
|Figure 10. A three-reach model|
|Figure 11. Two examples of degrees of connectivity in a three-reach model|
|Figure 12. Comparison of various ways of producing an average personal network of around 30|
|Figure 13. The parallelogram problem|
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