help > Pragmatic graph theory definitions
Sep 13, 2017  11:09 AM | Janelle Letzen - Johns Hopkins University
Pragmatic graph theory definitions
Hi Conn community,
I'm a newbie to the world of graph theory, so apologize in advance for the simplicity of these questions. I'm trying to wrap my head around some of basic terms in a practical way, and was wondering if someone can please confirm whether I'm understanding correctly, as well as answer a few questions.

If I'm properly understanding, nodes represent ROIs and edges represent significant r-to-Z correlations between two ROIs. Here are my questions:

1. It seems like most measures are agnostic of the magnitude of the edge (e.g., degree is the number of edges from one node, or number of significant correlations between one ROI and other ROIs in the graph). Do any metrics account for correlation magnitude?
2. Several resources described path length as the "distance" between two regions. I understand how this translates to the topology of a graph visually, but haven't been able to figure out what this means in terms of r-to-Z values. For example, would a shorter path length equate to greater r-to-Z magnitude between two ROIs without accounting for the influence of additional ROIs?
3. Some articles described a clustering coefficient as a measure of possible "triangles" around a node. Although this explanation again makes sense visually, I'm unsure of the pragmatic interpretation related back to correlation values. Do "triangles" represent ROIs with at least 3 significant r-to-Z correlations with nodes included in the model (so not accounting for relative correlation magnitude, just whether or not it is significant)?

I've read some seminal articles on this topic (e.g., Rubinov & Sporns, 2010; Bullmore & Sporns, 2012; Fallani et al., 2014; Wang et al., 2010), but would be grateful for additional resources that others have found helpful!

Thank you,
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Pragmatic graph theory definitions
Sep 13, 2017