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A vertex represents an atom and an undirected edge between two vertices represents a chemical bond.
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The simplest Feynman diagrams involve only two vertices, representing the emission and absorption of a field particle.
We label the vertices by basis elements, the existence of which is guaranteed by the Fundamental Theorem of Persistent Homology, and we draw an edge between two vertices to represent the maps (f_{i,j}), as explained in the main text.
One of the core ideas of IsoRank is that the similarity between two vertices may be determined by all the neighborhood vertices' similarity.
In the mechanism proposed in [15], first, a given network is transformed into a conflict graph whose vertices represent links and there is an edge between two vertices if two links conflict (interfere) with each other.
The vertices represent the AMP structures and an edge between two vertices exists if the TM-score > 0.5, indicating the two structures as the two verctices fall into the same fold [ 22].
The intuition behind the dps measure is to capture the ability to represent the taxonomic distance between two vertices with respect to the depth of the common ancestor of these two vertices.
In this graph, the vertices represent AMP structures and there is an edge between two vertices if the two AMP structures are similar.
The edges (i.e., connecting lines) represent the existence of interference between two vertices (readers).
For this application, the weights could represent the probabilities of having edges between two vertices.
Each network is represented by a graph whose vertices correspond to proteins, and there is an undirected edge between two vertices if and only if the corresponding proteins interact.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com