Topology of Cell-Aggregated Planar Graphs

Details Topology of Cell-Aggregated Planar Graphs Topology of Cell-Aggregated Planar Graphs

2006-05-18

arxiv.org/abs/cond-mat/0605455v1

Lecture Notes in Computer Science, Springer (Berlin) Part III, 3993 (2006) 1098-1105

Physics

Condensed Matter

Statistical Mechanics

8 pages, 5 figures

Scientific paper

10.1007/11758532_150

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.

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