Topology of Cell-Aggregated Planar Graphs

TL;DR

This paper introduces a new algorithm for growing non-clustered planar graphs through cell aggregation, analyzing their topological properties and relevance for nanopattern conduction.

Contribution

The paper presents a novel algorithm for planar graph growth with controlled topological features based on cell aggregation parameters.

Findings

Fractal dimension of the perimeter varies with aggregation parameters.

Distribution of shortest paths depends on cell size distribution.

Topological betweenness is influenced by chemical potential and cell size width.

Abstract

We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs--fractal dimension of the perimeter, distribution of shortest paths between pairs of nodes and topological betweenness of nodes and links. We show how these topological properties depend on the control parameters of the aggregation process and discuss their relevance for the conduction of current in self-assembled nanopatterns.