## 3 Results
### Bigraph Variability and Issue of Measure  
The R\({}_{\rm Q}\)-envelope and the bigraph are considered equivalent representations of seismograms. How, then, can we explain the issue of the variability of the bigraph? It is easy to notice bundles in the mesh of edges within the bigraph. Moreover, it is easy to identify bundles corresponding to respective groups of SFs just by comparing the output nodes of the bigraph with the shape of the R\({}_{\rm Q}\)-envelope. It is easy to grasp this idea by comparing Figures 3 and 4. There, it is easy to select the main bundle of edges, respective to SFs (i.e., SF(A)s, or \(A_{\rm max}\)s), which form the 'head' of the R\({}_{\rm Q}\)-envelope. There are also other bundles that can be identified. Relying on the claimed equivalence between the bigraph and the R\({}_{\rm Q}\)-envelope, it is easy to see that the R\({}_{\rm Qmax}\) corresponds to the biggest SF/SF(A) or to the rightmost output node \(n_{\rm K}\) in the bigraph (according to the convention of increasing values of SFs). The edge \(\epsilon_{\rm K}\), connected to the node \(n_{\rm K}\), designates the mapping of the largest SF/SF(A) and can be named as the structural axis of bigraph (spine, backbone), a reference for considering other edges or bundles of edges. Obviously, the meaning of these terms depends on the bigraph geometry, which, in this paper, is chosen to be a two-row structure with connecting lines between. Remembering the previous double indexing of output nodes, positional (mapped) and regular (see Figure 9), it is easy to measure each edge by simply subtracting the correspondent indices, for example:  
\[m_{\rm d}(n_{\rm K})=m_{\rm d}(24)=24-16=8\]  
This means that the mapping distance of the main node (max SF), which is labeled by index 16 (defining its position in input nodes), is translated (mapped) to position 24 (output nodes), which equals 8 units of displacement. Similarly, e.g., input node 7, which is mapped to position 20 of the output index string, which makes \(m_{\rm d}(20)=20-7=13\) units of displacement. For the given bigraph geometry, its height is \(H_{\rm b}\), and the mapping distance yields the edge slope:  
\[\alpha(n_{\rm K})=\alpha(24)=\arcsin(H_{\rm b}/m_{\rm d}(24))\]  
around which are arranged edges with similar slopes, making the primary bundles the main structural element of the bigraph (in its mesh). \[B_{0}=\{e_{k}:|\alpha(e_{k})-\alpha(e_{K})|\leq\delta,\ \forall k<K\} \tag{19}\]  
In that way, a relationship is established between the head in the diagram of \(R_{\rm Q}\) and the primary bundle in the bigraph mesh. In a similar way, one can define secondary bundles. Formatting of Bigraps  
One dimension of seismogram variability is its duration, which, when transferred into an \(R_{\rm Q}\) or bigraph, means the number of SFs or the bigraph size (number of nodes). Even a group of earthquakes defined by a certain set of grouping criteria shows heavy variability and prevents clustering. There are two proposals to equalize variable lengths of seismograms. **Extension of bigraph by empty complement**--It is well known from number theory and binary coding that, e.g., \(011=00000011\). Applying this simple idea to bipartite graphs, an empty bigraph is added to the current (actual) bigraph to attain the prescribed size. In other words:  
\[\#(BG_{\rm E(k)})=\#(BG_{\rm(k)})+\#(\rm E_{\rm(k)})=G,\ \forall k\]  
which one reads out as the size (\(G\)) of the extended bigraf is the sum of the sizes of the actual bigraf and its empty complement bigraph to attain a prescribed size (see Figure 21), constant for all bigraphs. Another parallel with the empty bigraph can be found in the set theory, with the empty set, but there are significant differences. The empty set has nothing in it but possesses only its existence, pointing to the fact that the set is a frame, and after that, it becomes a real set by containing certain elements. Figure 21: To illustrate the concept of the empty graph, the simple graph from Figure 4 is used, which is extended by an empty graph to the prescribed size.