In an article of the New York Times, James Gorman describes how Dr. Helen Mayberg, one of the many scientists who could use the MRI-database of the Human Connectome Project, use this term.
Are there several definitions of "critical node" in graph theory?
(NOTE: Article is in:
http://www.nytimes.com/2014/01/07/science/the-brain-in-exquisite-detail.html?_r=0 )
For any graph (connected graph), generally speaking, a "critical node" represents that node which, if it is extracted from the graph, the graph becomes unconnected.
The same meaning, this term must have everywhere.
I used the graphs connectivity on my researches in power systems. You can find an an illustrative example here, fig. 4: https://www.researchgate.net/publication/256190912_Fuzzy_Numbers_Based_Algorithm_for_Interruptions_Frequency_Estimation_on_Distribution_Smart_Grids?ev=prf_pub
Or: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=4218688&sortType%3Ddesc_p_Publication_Year%26queryText%3Db+tomoiaga
Conference Paper Fuzzy Numbers Based Algorithm for Interruptions Frequency Es...
Thank you for your answer.
That is the same meaning we used in our paper about the cortical graphs (Gomez and Lopera, 1999, "A topological...").
How often they use that term in power systems? what about "critical edge"? and "critical graph"? is there -in your context- a general feature characterized by the term "critical" in all these cases?
There is no "critical graph". There are just critical nodes (articulation points) and critical branches (isthmuses). The meaning is given by the topic of the problem.
Great! So the general feature of the term “critical element” (either for nodes or branches (edges)) might be: An element is critical when it is necessary to make a graph connected (i.e., if it is extracted, the graph becomes unconnected).
Please let me, then, reformulate the question: What about “critical subgraphs”? If the meaning is conserved, a critical subgraph represents a subgraph which, if it is extracted from the graph, the graph becomes unconnected.
In your illustrative example (fig 4, “Fuzzy numbers…”) you wrote about a way to reduce a graph to a “critical graph” (i.e. a graph only made with critical nodes and edges)…Is it –in this context- an example of a "critical graph" (in a "critical graph" every node or branch is a critical element)?
Oh, thank you, very interesting these basic definitions!
What about "critical subgraphs"? Are they the same than "subgraph separator"? Are they defined in this literature? If they do, do you think they follow a coherent feature (i.e. for vertices or for nodes or subgraphs)?
I see…is in this case “click” the same than “clique” (you know, a subset of vertices such that every two vertices in the subset are connected by an edge)?
In my question, cortical graphs are different to critical graphs. The first refers to the cerebral cortex (the outermost layered structure of the brain). A cortical graph is a mathematical representation where the cortical units (cortical modules or brain regions) are represented by nodes and the functional relations between nodes (estimated by node electrical activity, for instance) are represented by lines between these points (Med Hypotheses. 1999; 53(3):263-6. A topological hypothesis (...): A principle of the cortical graphs based on the neuroimaging Gomez JF, Lopera FJ).
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