The degree sequence of a scale-free random graph process

The degree sequence of a scale-free random graph process

Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwide web as follows: consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number of earlier vertices, selected with probabilities proportional to their degrees. In [2] and, with Jeong, in [3], Barabási and Albert suggested that after many step...

Degree-correlation of a Scale-free Random Graph Process

Barabási and Albert [1] suggested modeling scale-free networks by the following random graph process: one node is added at a time and is connected to an earlier node chosen with probability proportional to its degree. A recent empirical study of Newman [5] demonstrates existence of degree-correlation between degrees of adjacent nodes in real-world networks. Here we define the degree correlation...

The Degree Sequence of a Scale-Free Random Graph Process with Hard Copying

In this paper we consider a simple model of random graph process with hard copying as follows: At each time step t, with probability 0 < α ≤ 1 a new vertex vt is added and m edges incident with vt are added in the manner of preferential attachment; or with probability 1−α an existing vertex is copied uniformly at random. In this way, while a vertex with large degree is copied, the number of add...

Random Deletion in a Scale-Free Random Graph Process

We study a dynamically evolving random graph which adds vertices and edges using preferential attachment and deletes vertices randomly. At time t, with probability α1 > 0 we add a new vertex ut and m random edges incident with ut. The neighbours of ut are chosen with probability proportional to degree. With probability α − α1 ≥ 0 we add m random edges to existing vertices where the endpoints ar...

Popularity based random graph models leading to a scale-free degree sequence