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Studies of adaptive networks with preferred degree
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zia, R. K. P. Liu, Wenjia Jolad, Shivakumar Schmittmann, Beate |
| Copyright Year | 2011 |
| Abstract | We study a simple model involving adaptive networks in which the nodes add or cut links to other nodes according to a set preferred degree, κ. This behavior seems more natural for human beings as they form a circle of a preferred number of friends or contacts. In the simplest model, a node with degree k will add (cut) a link with probability w+ (k) (1 − w+ (k)). Several forms of w+ are considered, e.g., a step function that drops abruptly from unity to zero as k increases beyond κ. Using simulations, we find the degree distribution in the steady state. Unexpectedly, it is not a Gaussian (around κ). We are able to find an approximate theory which explains these distributions quite well. Introducing a second network and coupling the two in various ways, we find both understandable and puzzling features. In the third part, we consider overlaying an SIS model of epidemics on a single adaptive network, allowing κ to depend on the fraction of the infected population. The gross features of the resulting steady states can be well explained by a mean field like theory, balancing the rates of recovery and infection. Various avenues for further investigations are proposed. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www1.phys.vt.edu/~rkpzia/UGa2011.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation algorithm Arabic numeral 0 Cut (graph theory) Degree (graph theory) Degree distribution Equilibrium Node - plant part Normal Statistical Distribution Simulation Steady state |
| Content Type | Text |
| Resource Type | Article |
