# Kinetics of node splitting in evolving complex networks

Source: [Kinetics of node splitting in evolving complex networks](<https://www.sota2.com/research/paper/68fa2cb31e209131ce852660>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T15:31:06.902Z

Authors: E.R. Colman, G.J. Rodgers

Published: 2013-09-24T15:49:10.000Z

## Abstract

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each evolves at each time step by either preferential attachment, with probability $p$, or splitting with probability $1-p$. Two methods of attachment are considered; first, attachment of an edge between a newly created node and existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1309.6225>)

[PDF](<https://arxiv.org/pdf/1309.6225.pdf>)