Figure 1.
Projection Length Distribution and Total Wiring Length for Original and Rearranged Neural Networks
(A–C) Approximated projection length distribution in neural networks. Macaque monkey cortical connectivity network with 95 areas and 2,402 projections (A). Local distribution of connections within rostral ganglia of C. elegans with 131 neurons and 764 projections (B). Global C. elegans neural network with 277 neurons and 2,105 connections (C).
(D–F) Reduction in total wiring length by rearranged layouts yielded by simulated annealing for Macaque cortical network (D), C. elegans local network (neurons within rostral ganglia) (E), and global C. elegans network (F).
(G–I) Approximated projection length distribution in neural networks with optimized component placement. Macaque monkey cortical connectivity network (G). Local distribution of connections within rostral ganglia of C. elegans (H). Global C. elegans neural network (I). For all optimized networks, the number of long distance connections is reduced compared to the original length distribution in (A)–(C).
Figure 2.
Original and Optimally Rearranged Macaque Cortical Networks
(A) Original placement of 95 cortical areas.
(B) Network layout after evolutionary rearrangement of areas to minimize total wiring.
A larger version of this figure is available at http://www.biological-networks.org.
Figure 3.
Original and Optimally Rearranged Layouts of Local and Global Neural Networks of C. elegans
(A) Original placement of neurons within rostral ganglia.
(B) Optimized wire-saving component placement of rostral ganglia neurons.
(C) Original layout of global C. elegans network (lateral view).
(D) Global C. elegans neuronal network, rearranged to minimize total network wiring.
A larger version of this figure is available at http://www.biological-networks.org.
Table 1.
Network Measures for the Original Neural Systems as well as for Minimally Rewired Networks of the Same Size
Figure 4.
Network Properties of Original Cortical Networks and Minimally Rewired Networks of the Same Size Lacking Long-Distance Connections
Total wiring length (A) is substantially reduced in minimally rewired networks. Average metric length of the shortest path between any two nodes (B) is also lowered in the rewired networks. However, average path length (C), corresponding to the number of processing steps in the shortest path between components, is considerably smaller in the original than in the minimally rewired networks.
Figure 5.
Wiring Arrangement of Neural Networks Compared to Minimum and Maximum Case Benchmark Networks
(A) Actual total wiring length relative to the minimum wiring length solution (value “0,” yielded by simulated annealing of component positions) and to networks optimized for maximum total wiring length (value “1,” also yielded by simulated annealing). The wiring of the different neural networks lies close to the middle between minimum and maximum case component arrangements.
(B) Average shortest path length (characteristic path length) in neural networks relative to networks optimized for minimum path length (value “0,” yielded by simulated annealing of wiring organization) and maximum path length (value “1”). Actual path lengths in the neural networks are close to the lower bound of networks optimized for minimum paths.