On merging and dividing of Barabási-Albert-graphs

The Barabási-Albert-model is commonly used to generate scale-free graphs, like social networks. To generate dynamics in these networks, methods for altering such graphs are needed. Growing and shrinking is done simply by doing further generation iterations or undo them. In our paper we present four methods to merge two graphs based on the Barabási-Albert-model, and five strategies to reverse them. First we compared these algorithms by edge preservation, which describes the ratio of the inner structure kept after altering. To check if hubs in the initial graphs are hubs in the resulting graphs as well, we used the node-degree rank correlation. Finally we tested how well the node-degree distribution follows the power-law function from the Barabási-Albert-model.