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Fig. 1 | EURASIP Journal on Bioinformatics and Systems Biology

Fig. 1

From: Graph reconstruction using covariance-based methods

Fig. 1

a Transitive closure of a graph with four nodes. Solid edges indicate existing or direct edges in the graph, whereas dashed edges indicate indirect edges which are added to the graph as the result of the transitive closure effect. b Three-dimensional true graph (left), the transitive closure of the true graph (middle), and the corresponding covariance graph constructed from the covariance matrix (right). c The illustration of a star graph. d (left) The true example graph which corresponds to the concentration graph, G, and (right) the covariance graph, \(\tilde {G}\) constructed from the covariance matrix. The true graph is sparse, and the covariance graph is fully connected. e The covariance graph, \(\tilde {G}\) with edge weights given by the correlation matrix C (the graph is predicted by thresholding the correlation matrix). (left) The graph structure when the condition (A.11) holds (see Additional file 1). (right) The graph structure when (A.12) holds (see Additional file 1). Distribution of direct and indirect edges of the covariance graph (p=500), when f \(A_{i(i+1)} \sim \mathcal {N}(0.4,0.0005), \ i=1,\ldots, p-1\) and g \(A_{i(i+1)} \sim \mathcal {N}(0.4,0.5), \ i=1,\ldots, p-1\). Vertical line (blue) indicates the optimal threshold that separates two distributions (For more information about e, f, and g, see the text in the Additional file 1)

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