Aspects of Randomness in!Neural Graph Structures

*Michelle Rudolph-Lilith!Lyle E Muller

JournalClub :: Gif-sur-Yvette :: 2013/04/08

Graph-Theory Preliminaries!

number of nodes

Graph-Theory Preliminaries!

number of nodesnumber of edges

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

1

32

4

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

total adjacency

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

total adjacency

connectedness

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

total adjacency

connectedness

asymmetry index

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

total adjacency

connectedness

asymmetry index

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

total adjacency

connectedness

asymmetry index

undirected!graph

Graph-Theory Preliminaries!

number of nodesnumber of edgesadjacency matrix

total adjacency

connectedness

asymmetry index

undirected!graph

neural graph

C. elegans

CE1 306 2345CE2 297 2345

CE3 279 2996

CatCC1 95 2126CC2 52 818

Macaque

MB1 383 6602MC1 71 746

MC2 94 2390

MNC1 47 505

MVC1 30 311

MVC2 32 315

Historical Neural Graphs!

MB1

Adjacency, Connectedness, Asymmetry!

CE3

Adjacency, Connectedness, Asymmetry!

Adjacency, Connectedness, Asymmetry!

CE3undirected

Adjacency, Connectedness, Asymmetry!

Adjacency, Connectedness, Asymmetry!

for random graphs:

Node-Degree Distributions!

node-degrees

directed

undirected

Node-Degree Distributions!

fitting models

Node-Degree Distributions!

node in-degree node out-degree node-degree

CE3

Node-Degree Distributions!

node in-degree node out-degree node-degree

CC1

Structural Equivalence!

Euclidean distance

Pearson correlation coefficient

Structural Equivalence!

for random graphs: for random graphs:

Structural Equivalence!

correlation coefficientof node end-degrees

Structural Equivalence!

Nearest Neighbor Degrees!

average nearest neighbor degrees

directed

undirected

Nearest Neighbor Degrees!

Nearest Neighbor Degrees!

assortativity coefficient

Nearest Neighbor Degrees!

Summary and Conclusion!

node degree distributions are in accordance with a gamma model, supporting the idea of a simple local mechanism responsible for generating neural graphs

structural equivalence analysis suggests independent random distribution of node connections for different nodes, but strong correlations between in-coming and out-going connections for the same node

a weak disassortative tendency was observed, suggesting that in neural graphs nodes tend to connect with nodes of slightly higher degree

Contrary to many results reported in the neuroscientific literature, structural neural graphs show a consistency with randomness, as opposed to a consistency with more abstract models of graph construction, such the scale-free graph!