Multi-edges-wheel graph05C8505C30In order to solve a problem, a usual approach is to represent it in a simple structure and bring it to some particular cases. In graph theory, this approach is used to illustrate
In the chemical graph of drug structure, atoms represent vertices, while the bonds that connect them are known as edges. The graphG(V,E)is considered to be simple and linked. The lettersVandEstand for vertex and edge set, respectively. The degree of a vertexvis indicated bydvand represents...
For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e∉G, there is a copy of F in G+e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n,F). A graph G is weakly F-saturated if G ...
Subdividing the edges of G tends to favour the cop both by slowing down the robber’s movement around the graph and by giving her extra vertices to probe. Another way in which we might make the game easier for the cop is to allow her to choose a set of k vertices to probe at each...
In the basic scenario, illustrated in Fig. 1, the communication network is described by a directed graph, where the vertices represent communicating parties and the edges represent communication channels between them. When a communication channel is not used, we will model its input as being the ...
In single-cell RNA sequencing (scRNA-Seq), gene expression is assessed individually for each cell, allowing the investigation of developmental processes, such as embryogenesis and cellular differentiation and regeneration, at unprecedented resolution. In
A network is a mathematical object from graph theory consisting of nodes connected in pairs by edges. Networks are a useful tool for representing pairwise relationships in various social or physical systems in an abstract manner, and consequently, network approaches have been widely applied to study...
Therefore, edges in the graph represent (k+1)-mers. A de-Bruijn graph of multiple sequences is the union of the de-Bruijn graphs for each individual sequence. Locally colinear block construction Given a set of anchors represented as a graph, the next step is to identify locally colinear ...
Each modality can be represented as nodes, and edges can be defined based on the relationships or correlations between modalities [96]. Graph-based algorithms, such as graph convolutional networks (GCNs) or graph regularized non-negative matrix factorization (GNMF), can then be applied to capture...
In addi- tion, we show that these activations were obtained with both better and poorer eye fixation behavior (Extended Data Fig. 3), indicating that the results were not an artifact of eye movements and that they were not because of edges of the spot stimuli or subtraction of the fixation...