Symbol B
B is part of the quantity the equation computes from the expression on the right.
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Why this formula appears here
What r is actually sensitive to follows from the same argument in reverse. The null space of B has dimension equal to the number of connected components of the network graph; for a connected network it is exactly one-dimensional, spanned by the all-ones vector, because B = 0 forces = across every edge and connectivity propagates that equality to every node. By rank–nullity, a connected tree — with exactly |V|-1 edges for |V| nodes — has an incidence matrix of full row rank, meaning that for any data whatsoever a exists reproducing it exactly. A tree, in other words, cannot fail to close, on any data, ever; it carries zero redundant edges and therefore zero capacity to…
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Symbol phi
phi is part of the quantity the equation computes from the expression on the right.
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Read it with the definitions, units, and assumptions supplied by the article.
Published contexts (1)
A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.
Equation 44 · Evolutionary Physics
The Bend an Elevator Cannot Fake
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.
What r is actually sensitive to follows from the same argument in reverse. The null space of B has dimension equal to the number of connected components of the network graph; for a connected network it is exactly one-dimensional, spanned by the all-ones vector, because B = 0 forces = across every edge and connectivity propagates that equality to every node. By rank–nullity, a connected tree — with exactly |V|-1 edges for |V| nodes — has an incidence matrix of full row rank, meaning that for any data whatsoever a exists reproducing it exactly. A tree, in other words, cannot fail to close, on any data, ever; it carries zero redundant edges and therefore zero capacity to…
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