Figure 1

Summary on the eight types of MTB. The different types are named according to (1) whether the defining submatrix of an MTB can only contain 1’s (restrictive, R) or is allowed to contain 0’s (loose, L), and (2) whether the miRNAs (mi) are not allowed to have extra targets, the mRNAs (m) are not allowed to be targeted by extra miRNAs, or the general case (gen) that both are allowed. In the formal mathematical definitions, r and c correspond to the sets of row and column indices defining an MTB, where each row corresponds to an mRNA and each column corresponds to a miRNA. a _ij is the value at row i and column j of the adjacency matrix. In the matrix representation, an example is shown for each type of MTB, where the sub-matrix enclosed by the rectangle corresponds to the example MTB. For visualization purpose, they are drawn to occupy consecutive rows and columns, but this is not required in the actual definitions of the MTB types. Values of irrelevant cells, i.e., those not on the rows and columns defining the MTB, are omitted. In the graphical representation, the red nodes are the mRNAs and miRNAs defining the example MTB, red lines are edges between them, and blue lines are edges connecting them to mRNAs or miRNAs outside the MTB. In the formulas for showing the number of MTBs of each type, R and C are the full sets of miRNAs and genes in the miRNA-target network, respectively, and |R| and |C| are their sizes. The function connected(i,j) means the nodes in the graphical representation corresponding to row i and column j are connected, which can be formally defined as $\exists i_1,i_2,\mathrm{...},i_k\in r,j_1,j_2,\mathrm{...},j_k\in s,\mathrm{s.t.}{a}_{{\mathit{\text{ij}}}_1}=a_{i_1{j}_1}=a_{i_1{j}_2}=a_{i_2{j}_2}=\mathrm{...}=a_{i_k{j}_k}=a_{i_{k}j}=1$.