Addition-Deletion Networks

TL;DR

This paper analyzes a dynamic network model where nodes are both added and deleted, revealing how these processes influence network structure, degree distribution, and the emergence of a giant hub.

Contribution

It introduces a new model of growing networks with simultaneous addition and deletion, deriving analytical results for degree distribution and structural properties.

Findings

In-component size distribution follows a power law with a variable exponent.

The network develops a giant hub due to deletion dynamics.

Structural properties like height and diameter are analytically characterized.

Abstract

We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly selected existing node. With rate 1, a randomly selected node is deleted, and its parent node inherits the links of its immediate descendants. We show that the in-component size distribution decays algebraically, c_k ~ k^{-beta}, as k-->infty. The exponent beta=2+1/(r-1) varies continuously with the addition rate r. Structural properties of the network including the height distribution, the diameter of the network, the average distance between two nodes, and the fraction of dangling nodes are also obtained analytically. Interestingly, the deletion process leads to a giant hub, a single node with a macroscopic degree whereas all other nodes have a microscopic degree.