Different ways to represent a static graph. Beyond the adjacency matrix representation as shown in Figure 2 (E-H), a static graph can be also represented as an "adjacency list" or "incidence matrix".

Different ways to represent a static graph. Beyond the adjacency matrix representation as shown in Figure 2 (E-H), a static graph can be also represented as an "adjacency list" or "incidence matrix".

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Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and heterogeneous characteristics of industrial size networks. Graph embedding techniques can be effective in converting...

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... Incidence matrix: It employs a |V | × |E| matrix to represent the relationship between node set and edge set in a graph. More details can be seen in Figure 3, where each column denotes different edges, and each row denotes different nodes in a directed graph. Each element in the matrix can be filled with ("1"-the column edge is one outgoing edge from the row node; "0"-the column edge is not connected with the row node; "-1"-the column edge is one incoming edge to the row node (for undirected graphs, elements with "-1" are all filled with "'1'). ...
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... workflow consists of multiple steps and begins by preprocessing the Hi-C interaction data to output a normalized intercromosome matrix based on which the interaction graph is constructed. A schematic of this workflow is shown in Figure 13 (A). Areas (genomic bins) with the same chromosome are represented by the same color nodes. ...
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... and system-level changes for 12 patients before and after MDCT intervention based on MG2G (blue) and node2vec [16] (yellow, green, and red correspond to different node2vec parameters); (C) MG2G result: Violin plot for the W2-distance distributions and probability densities of all 264 regions w.r.t. different patients (the embedding size L = 16). Fig. 13. Example of applying the deterministic LINE graph embedding method for subcompartment identification using Hi-C chromatin interaction data. (A) Workflow from left to right proposed by [1], showing a normalized Hi-C interchromosome matrix used to construct the interaction graph. The nodes with the same color denote genomic bins from the ...
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... method proposed in [1] based on LINE embedding outperforms the hidden Markov model (HMM) for sub-compartment prediction, and in fact it predicts a larger number (9 versus 5) of sub-compartments. It also outperforms two other graph embedding methods that we described in this review paper, namely HOPE [37] and DeepWalk [39], as shown in Figure 13 (B-D). Genomic regions that map to the same sub-compartment based on the graph embedding method are spatially close to each other. ...
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... Silhouette index ranges from −1 to 1, with a higher value indicating better clustering performance. The LINE method [48] improves the Silhouette index compared to HMM and is also superior to HOPE and DeepWalk with respect to all three metrics as shown in Figure 13 (B-D). ...

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