[SOUND] So, in many situations, we like to create networks consisting of large
numbers of non-overlapping brain regions.
So network analysis tries to characterize these networks using a small number of
meaningful summary measures.
You might take a big network and try to summarize it using a few summary measures
that we can compare across subjects or groups.
The hope is that the comparison of these network topologies between groups of
subjects might possibly reveal connectivity or
abnormalities related to neurological or psychiatric disorders.
To recall, networks can be represented using graphs, which are mathematical
structures used to model pair-wise relationships between variables.
They consist of a set of nodes, or vertices, V, and the corresponding links,
or edges, E, that connect pairs of vertices.
So a graph, G, which is equal to V and E, which is the collection of the nodes and
links, may be defined as either undirected or
directed with respect to how the edges connect one vertex to another.
In addition, the edges may be either binary, just 0 or 1, or
weighted, depending on the strength of the connection.
It's generally beneficial to represent a brain network using an nxn matrix,
where n is the number of nodes.
Here the graph nodes are represented by columns and rows of the matrix.
And a link between two nodes, i and j, is represented by matrix element (i,j).
Here's an example of a network.
So this is a bi-directional network between three different nodes, A,
B, and C.