1. Neural Network of C. elegans is a Small-World Network Masroor Hossain Wednesday, February 29 th, 2012 Introduction to Complex Systems

2. Background on C. elegans It’s a transparent nematode (roundworm). The hermaphrodite version has a simple nervous system comprising about 302 neurons. It’s neural network is completely mapped. The pattern of connectivity portrays small- world network characteristics.

4. Recall The characteristic path length L is defined as the number of edges in the shortest path between two vertices, averaged over all pairs of vertices. The clustering coefficient C measures the degree to which nodes in a graph tend to cluster together - how close neighbors are to being a clique.

5. Procedure for Measuring C – from class

6. Random Rewiring Procedure p = 0 represents regularity (no edge) p = 1 represents disorder (clique) n = 20 and k = 4

7. Random Rewiring Procedure For C. elegans, an edge/link joins two neurons if they are connected by a synapse or gap junction. There are n = 282 nodes and k = 14 edges.

8. NetLogo Models

11. Cumulative Distribution of Outgoing and Incoming Neural Connections

12. Questions?