Structural properties of networks grown via an Achlioptas process
After the Achlioptas process (AP), which yields the so-called explosive percolation, was introduced, the number of papers on percolation phenomena has been literally exploding. Most of the existing studies, however, have focused only on the nature of phase transitions, not paying proper attention to the structural properties of the resulting networks, which compose the main theme of the present paper. We compare the resulting network structure of the AP with random networks and find, through observations of the distributions of the shortest-path length and the betweenness centrality in the giant cluster, that the AP makes the network less clustered and more fragile. Such structural characteristics are more directly seen by using snapshots of the network structures and are explained by the fact that the AP suppresses the formation of large clusters more strongly than the random process does. These structural differences between the two processes are shown to be less noticeable in growing networks than in static ones.
KeywordsAchlioptas process Complex networks Structural properties
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- In the same sense, N nodes are randomly wired with L links.Google Scholar
- M. E. J. Newman, Networks: An Introduction (Oxford University Press, New York, 2011).Google Scholar
- There are several versions of the AP with small differences in the details of the link selection methods [13,15, 17].Google Scholar
- In order to study the network structure of the macroscopic-size of the giant component that exists above the percolation threshold δ c, we use the link density δ = L/N = 1 (correpsonding to the average degree 〈k〉 = 2), which is larger than δ c for all four processes considered in this work.Google Scholar