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It is possible to obtain a random reference for the comparison between any two adjacency matrices A and B as follows.
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To quantify the effects of prior knowledge incorporation, we use graph edit distance [ 24] between two adjacency matrices as a measurement for the dissimilarity of two graphs.
In order to provide a more balanced overall measurement of the similarity between two adjacency matrices A and B, both with the same dimension N × N, we consider the geometrical average g(A, B) between the ratios of correct ones (R1) and correct zeros (R0).
The adjacency structure between any two orthants reflects the edges shared by the two corresponding topologies and permits the definition of paths visiting several orthants.
Using the topological overlap measure as opposed to the raw adjacency values minimizes the effects of spurious connection strengths between any two genes.
In the following, by considering the resistance distance between any two vertices, we first define the Kirchhoff matrix Kf A ( G ) as a weighted adjacency matrix.
Then, the adjacency matrix is transformed into a topological overlap matrix (TOM), which summarizes the degree of shared connections between any two genes, and then converted into a dissimilarity matrix.
Maximum spacing between any two selected stations.
Minimum spacing between any two selected stations.
The adjacency between two points is defined as 1−[dist / max dist)], where dist denotes Euclidean distance between the points and max dist) denotes the maximum distance between any two points.
In other words, a DCJ rearranges two adjacencies in A, transforming them into two new adjacencies.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com