Topology of Cell-Aggregated Planar Graphs

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.

arXiv comment8 pages, 5 figures

References in corpus (3)

• The structure and function of complex networks
• Evolution of networks
• Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?

Cited by in corpus (4)

• Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
• Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops
• Collective Charge Fluctuations in Single-Electron Processes on Nano-Networks
• Inductive Construction of 2-Connected Graphs for Calculating the Virial Coefficients