## 3 Results and Discussion  
### Half-Space Proximal Network Model  
HSPNs of ABFPs were built with the Euclidean distance metric, but changing similarity threshold from 0.0 to 0.95. As long as the cutoff increases, the network density decreases due to the loss of edges satisfying the similarity cutoff. Therefore, several nodes become disconnected from the giant component of the network, and appear as isolated communities or singletons representing atypical sequences. The original HSPNs (with no similarity cutoff) have the particularity that all nodes are fully connected, as in the giant components of half-space graphs; however, upon applying increased similarity cutoffs, increasingly sparser graphs with unconnected nodes (singletons) are displayed. Then, some network parameters were retrieved at different similarity cutoffs in order to determine the optimal parameter for determining the most informative network topology. In relevance order, network parameters such as density, modularity, average clustering coefficient and number of communities were analyzed (Figure 2). The network density is the actual number of edges over the maximum number of possible edges in a network. If the density is too high, the understanding of network topological features becomes complicated, and if it is too low, then get loses useful information; therefore, a compromise between both extremes is needed. Generally, a network density of around 0.1 is acceptable; however, HSPNs are sparser netw  
Figure 2: Behavior of HSPNs parameters representing the 174 ABFPs when the similarity cutoff varies from 0 to 0.95.  
density values (<0.01). HSPNs are non-classical similarity networks because their node connections are determined by a predefined half-space proximal (HSP) test that generates a connected network but that only uses a small fraction of the maximum number of possible edges. More detailed information about the HSPNs construction can be found at [36]. Considering they are sparser networks by definition, upon increasing the similarity cutoff, HSPNs' density tends to drop even more, only retaining a reduced number of edges weighted with high similarity. The modularity of the networks was also analyzed at each similarity cutoff. This is a network parameter that compares the density within a community with the expected density for the same group of nodes in a random network. We calculated modularity and the number of communities using the modularity optimization clustering algorithm (based on the Louvain method [40]). Unlike the network density, both the modularity and the number of communities/singletons are significantly increased, especially upon applying similarity cutoffs from 0.5 (Figure 2). On the other hand, the average clustering coefficient (ACC) is a global measure of nodes' neighborhood connectivity and can also be used for evaluating network topology changes against similarity thresholds. Although at a similarity cutoff of 0.80 all network parameters displayed a dramatical change (Figure 2), the optimal value was selected by jointly analyzing all HSPN parameters and topologies (Supplementary File S1). The point at which the network density dramatically drops but at the same time the modularity increases (while considering the trade-off between the number of communities/singletons generated) is a good starting criterion for selection. In this sense, the cutoff value should be between 0.6-0.7, where the density and modularity have an inverse behavior, while the ACC does not suffer any dramatic change and the number of communities and singletons are reasonable in order to display an informative network topology (Figure 2). Thus, the optimal cutoff of 0.65 was selected by analyzing all the HSPN parameters displayed in Figure 1 and Supplementary File S1, and the networks' topologies as well.