## Random Deletion In A Scale Free Random Graph Process (2004)

Citations: | 16 - 3 self |

### BibTeX

@MISC{Cooper04randomdeletion,

author = {Colin Cooper and Alan Frieze and Juan Vera},

title = {Random Deletion In A Scale Free Random Graph Process},

year = {2004}

}

### OpenURL

### Abstract

We study a dynamically evolving random graph which adds vertices and edges using preferential attachment and deletes vertices randomly. At time t, with probability #1 > 0 we add a new vertex u t and m random edges incident with u t . The neighbours of u t are chosen with probability proportional to degree. With probability # 0 we add m random edges to existing vertices where the endpoints are chosen with probability proportional to degree. With probability 1 #0 we delete a random vertex, if there are vertices left to delete. and with probability #0 we delete m random edges. Assuming that #+#1 +#0 > 1 and #0 is su#cently small, we show that for large k, t, the expected number of vertices of degree k is approximately dk t where as k ##, dk Ck -1-# where # = 2(#-# 0 ) 3#-1-# 1 and C > 0 is a constant. Note that # can take any value greater than 1. 1