Neural Network of C. elegans is a Small-World Network

Masroor HossainWednesday, February 29th, 2012Introduction to Complex Systems

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.

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.

Procedure for Measuring C – from class

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

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.

NetLogo Models

Cumulative Distribution of Outgoing and Incoming Neural Connections

Questions?