Uncovering New Drug Properties in Target-Based Drug–Drug Similarity Networks

Despite recent advances in bioinformatics, systems biology, and machine learning, the accurate prediction of drug properties remains an open problem. Indeed, because the biological environment is a complex system, the traditional approach—based on knowledge about the chemical structures—can not fully explain the nature of interactions between drugs and biological targets. Consequently, in this paper, we propose an unsupervised machine learning approach that uses the information we know about drug–target interactions to infer drug properties. To this end, we define drug similarity based on drug–target interactions and build a weighted Drug–Drug Similarity Network according to the drug–drug similarity relationships. Using an energy-model network layout, we generate drug communities associated with specific, dominant drug properties. DrugBank confirms the properties of 59.52% of the drugs in these communities, and 26.98% are existing drug repositioning hints we reconstruct with our DDSN approach. The remaining 13.49% of the drugs seem not to match the dominant pharmacologic property; thus, we consider them potential drug repurposing hints. The resources required to test all these repurposing hints are considerable. Therefore we introduce a mechanism of prioritization based on the betweenness/degree node centrality. Using betweenness/degree as an indicator of drug repurposing potential, we select Azelaic acid and Meprobamate as a possible antineoplastic and antifungal, respectively. Finally, we use a test procedure based on molecular docking to analyze Azelaic acid and Meprobamate’s repurposing.


Introduction
Conventional drug design has become expensive and cumbersome, as it requires large amounts of resources and faces serious challenges [1,2]. Consequently, although the number of new FDA drug applications (NDAs) has significantly increased during the last decade-due to a spectacular accumulation of multi-omics data and the appearance of increasingly complex bioinformatics tools-the number of approved drugs has only marginally grown (see Figure 1) [3,4], calling for more robust alternative strategies [5]. 1940 1950 1960 1970 1980 1990  We used the FDA's annual reports data [6] and removed local oscillations by plotting a polynomial data fitting.
One of the most effective alternative strategies is drug repositioning (or drug repurposing) [7,8], namely finding new pharmaceutical functions for already used drugs. The extensive medical and pharmaceutical experience reveals a surprising propensity towards multiple indications for many drugs [9], and the examples of successful drug repositioning are steadily accumulating. Out of the 90 newly approved drugs in 2016 (a 10% decrease from 2015), 25% are repositionings in formulations, combinations, and indications [4]. Furthermore, drug repositioning reduces the incurred research and development (R&D) time and costs and medication risks [9,10].
The recent developments confirm computational methods as powerful tools for drug repositioning: • The trivialization/spread of omics analytical approaches have generated significant volumes of useful multi-omics data (genomics, proteomics, metabolomics, and others) [11,12].

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The ubiquity of digitalization in everyday life, including social media, has tremendously expanded the amplitude of the process of gathering data on drug-drug interactions and drug side-effects [13,14].

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The recent developments in physics, computer science, and computer engineering have created efficient methods and technologies for data exploration and mining, such as complex network analysis, machine learning, or deep learning [12,[15][16][17][18][19].
Complex network analysis has proven to be a useful tool for predicting unaccounted drug-target interactions. Indeed, several state-of-the-art network-based computational drug repurposing approaches use data on confirmed drug-target interactions to predict new such interactions, thus leading to new repositioning hints [20,21]. Some approaches build drug-drug similarity networks, where the similarity is defined based on transcriptional responses [22,23]. These repositioning approaches analyze the network parameters and the node centrality distributions in either drug-drug or drug-target networks, using statistical analysis [11,12,24,25] and machine learning (i.e., graph convolutional networks) [26][27][28][29] to link certain drugs to new pharmacological properties. However, conventional statistics can be misleading when used to predict extreme centrality values, such as degree and betweenness (which particularly indicate nodes/drugs with a high potential for repositioning) [30]. Nonetheless, other previous network-related approaches introduce useful repositioning pipelines [31,32], but they are mostly based on multi-partite and multilayered unweighted networks, challenging to process and interpret.
To overcome these challenges, we developed a novel, network-based, computational approach to drug repositioning. To this end, we build a weighted drug-drug network, i.e., a complex network where the nodes are drugs, and the weighted links represent relationships between drugs, using information from the accurate DrugBank [33]. In our drug-drug similarity network (DDSN), a link is placed between two drugs if their interaction with at least one target is of the same type (either agonistic or antagonistic). The link weight represents the number of biological targets that interact in the same way with the two drugs.
Our methodology for analyzing the drug-drug similarity network (DDSN) consists of the following steps: 1.
Generate (using the Force Atlas 2 layout and modularity classes) [34,35] both topological clusters and network communities.

2.
Relate each cluster and each community to a pharmacological property or pharmacological action (i.e., label communities and clusters according to the dominant property or pharmacological action), using expert analysis.

3.
Identify and select (by betweenness divided by degree, b/d) within each topological cluster/modularity class community, the top drugs not compliant with the cluster/community label. Network analysis uses centralities to rank nodes (i.e., drugs); we opt for the b/d centrality to find this centrality's distribution more stable in the DDSN.

4.
Validate the hinted repositionings by searching the new versions of DrugBank, the electronic records containing the relevant scientific literature (for merely reconstructed repositionings), and by analyzing molecular docking parameters [36] for previously unaccounted repositionings.
This way, we assessed our method's ability to uncover new repositionings by confronting the results with the latest (version 5.1.4) Drug Bank and data compiled from interrogating scientific literature databases.

Building the DDSN
We built our DDSN as a weighted graph G = (V, E), where V is the vertex (or node) set, and E is the edge (or link) set; the vertices (nodes) represent drugs and the edges (links) represent drug-drug similarity relationships based on drug-target interactions. G has |V| vertices v i ∈ V and |E| edges e j,k ∈ E, with i, j, k ∈ {1, 2, . . . |V|} and j = k. Each edge e j,k is characterized by a weight w(e j,k ) = 0 (in an unweighted network, w(e j,k ) = 1, ∀e j,k ∈ E). In our weighted DDSN, the weight represents the degree of target action similarity between drugs v j and v k , and it is equal with the number of common biological targets for v j and v k . Consequently, w(e j,k ) ∈ N * , ∀e j,k ∈ E. If e j,k = 0, then there is no target similarity between v j and v k , therefore no edge between these nodes. A common biological target is a target t k ∈ T (T is the set of targets) on which drugs v j and v k act in the same way, either both agonistically or both antagonistically. Figure 2 illustrates the building of the DDSN with information on drug-target interactions.
For the DDSN graph G, we use the drug-target interaction information from Drug Bank 4.2 [33]. We base our analysis on the largest connected component of the DDSN, consisting of |V| = 1008 drugs/nodes and |E| = 17963 links resulted from the analysis of the drug-target interactions with |T| = 516 targets. We opted for the older Drug Bank version 4.2 [33], to be able to use the latest Drug Bank 5.1.4 [37] for testing the accuracy of our drug property prediction. . An illustrative example of using drug-target interaction information to build a weighted drug-drug similarity network. In panel (a), we consider the drug-target interactions between four drugs (i.e., round nodes labeled 1 to 4) and three targets (i.e., square nodes labeled 1 to 3). The dashed red links represent agonist drug-target interactions, whereas the solid blue links represent antagonist drug-target interactions. In panel (b), we show the DDSN corresponding to the interactions in (a). For instance, a link of weight 3 connects the nodes 1 and 2 because Drug 1 and Drug 2 interact in the same way for the three targets, i.e., agonist on Target 2 and antagonist on Targets 1 and 3. Furthermore, a link with weight 2 connects Drug 2 and Drug 4 because they both interact agonistically on Target 2 and antagonistically on Target 1, but they do not interact in the same way with Target 3. In panel (c), we show a DDSN sub-network example, according to drug-target interactions from DrugBank 4.2, containing drugs Dextromethorphan, Felbamate, Tapentadol, Tramadol, and Memantine. We shape the link thickness according to the weight and specify the list of common targets for each link. The weight equals the number of targets in the list, where t 1 = Glutamate receptor ionotropic NMDA 3A, t 2 = Glutamate receptor ionotropic NMDA 2A, t 3 = Glutamate receptor ionotropic NMDA 2B, t 4 = Alpha-7 nicotinic cholinergic receptor subunit, t 5 = Mu-type opioid receptor, t 6 = Kappa-type opioid receptor, t 7 = Delta-type opioid receptor, t 8 = Sodium-dependent noradrenaline transporter, and t 9 = Sodium-dependent serotonin transporter.

Network Analysis
This paper uses complex network analysis tools to uncover new drug properties from the drug-target data. We employ network clustering (i.e., network community detection) to associate drugs with previously unaccounted drug properties and network centralities to prioritize the uncovered drug repurposing hints.

Network Clustering
The network clustering classifies each node v i ∈ V in one of the disjoint sets of nodes (cluster C i ⊂ V, with i = 1..m, C 1 C 2 . . . C m = V). In [35], the authors use modularity to define the node membership to one of the clusters. To this end, the modularity of a clustering C m = {C 1 , where |E| is the total number of edges in G, |E C i | is the total number of edges between nodes in cluster C i , d is the total degree of nodes in G, and d C i is the total degree of nodes in cluster C i . Thus, represents the edge density of cluster C i relative to the entire network G density, whereas We perform clustering using the software package Gephi [38], by maximizing the modularity from Equation (1) with the method introduced and analyzed in references [39,40]. The approach is to divide a graph into two communities, such that we get maximum modularity. The binary method can then be applied recursively on each resulted community, thus dividing them further; the entire process comes to an end when we cannot further increase the overall modularity. To describe the division algorithm, we write the graph modularity as In Equation (2), A ij is the graph's adjacency matrix, d i and d j are respectively the degrees of vertices/nodes v i and v j , and k is the total number of edges in the network (k = |E| = 1 2 ∑ i d i for an unweighted network). Furthermore, s i = 1 if v i is classified in community 1 and s i = −1 if v i is classified in community 2 [41]. Therefore, we have 1 2 s i s j + 1 = 1 if v i and v j are in the same community 0 otherwise .
For a detailed description of the clustering algorithm, please refer to the pdf Supplementary Information, Section S1.
Because our network is weighted, each edge has a weight w(e i,j ) = w i,j ∈ R * , and we rewrite Equation (1) as In Equation (4), w E is the total edge weight of edges E in G, w E C i is the total edge weight of edges in cluster C i , w V is the total edge weight of all vertices V in G, and w C i is the total edge weight of vertices in cluster C i .
A network layout algorithm places each vertex v i in a 2D space R × R = R 2 . Therefore, each node v i ∈ V has its 2D coordinates γ i = (x i , y i ) ∈ R 2 , and each edge e i,j ∈ E has a Euclidian distance In an energy-model, force-directed layout, we have a force of attraction between any two adjacent nodes v i and v j , and a repulsion force between any two non-adjacent nodes. The expression of these forces is |γ i − γ j | f # » γ i γ j , where f = a for attraction and f = r for repulsion. The attraction force between adjacent nodes (v i and v j such that ∃e i,j ∈ E) decreases, whereas the repulsion force between non-adjacent nodes (v i , v j such that ∃!e i,j ∈ E) increases with the Euclidian distance. Therefore, we must have a ≥ 0 and r ≤ 0.
In this paper, we use the energy-model force-directed layout Force Atlas 2 [34] to assign node positions in the 2D (i.e., R 2 ) space, based on interactions between attraction and repulsion forces, such that we attain minimal energy in the network layout, The energy-based layouts generate topological communities because specific regions in the network have larger than average link densities. Noack [41] demonstrated that the energy-based topological communities are equivalent to the network clusters based on modularity classes [35], when a > −1 and r > −1. Furthermore, given that our DDSN is a weighted network, we rewrite Equation (5) accordingly, to maintain equivalency with Equation (4), where w i and w j represent the total weight of edges incident to nodes v i and v j (i.e., the weighted degree of vertices v i and v j ), respectively, while w i,j is the weight of edge e i,j .

Network Centralities
Node centralities are complex network parameters that characterize the vertex/node's importance in a graph [42]. In our analysis, we considered the weighted degree, degree, betweenness, and betweenness/degree node centralities, to find that betweenness/degree is appropriate for the prioritizing of drug repositioning hint tests. Reference [43] shows that the betweenness/degree centrality is a crucial driver of complex network dynamics.
The weighted degree of a node v i is the sum of the weights characterizing the links/edges incident We compute the degree of a node v i with Equation (7), assuming that w e i,j = 1, ∀e i,j ∈ E.
To compute the node betweenness, we must find the shortest paths between all node pairs v j , v k in graph G, namely σ j,k . As such, the betweenness of node v i is the number of minimal paths in graph G that cross node v i , divided by the total number of minimal paths in G, where the total number of shortest paths in G is the combinations of 2 vertices from V, The betweenness/degree of node v i is the ratio where Equation (7) computes d (v i ) in the unweighted version (i.e., considering w e i,j = 1, ∀e i,j ∈ E).

Molecular Docking for Repurposing Testing
The effectiveness of out network-based drug repurposing prediction method is emphasized by the fact that DrugBank 4.2 confirms the properties we predict for 59.52% of the drugs, and 26.98% are existing drug repositioning hints we reconstruct with our DDSN approach (confirmed by the later DrugBank 5.1.4 and recent scientific literature). The remaining 13.49% of the drugs seem not to match the predicted pharmacologic property; therefore, we consider them potential drug repurposing hints that need to be tested in silico, in vitro, and in vivo. Here, we propose a preliminary testing method based on molecular docking simulations.

Testing Procedure
To verify the predicted properties of any repurposing hint, we perform molecular docking not only for the hint but also for the reference drugs (typical drugs having the predicted property) and some drugs with little probability of having the predicted property. To this end, we formalize the following testing procedure.

1.
We define the drug sets to enter the docking process, consisting of drugs hinted as having the pharmacological property φ (D n contains typical drugs for other pharmacological properties, with little probability of having property φ.

2.
We establish the target sets. Specifically, for pharmacological property φ, we take into consideration the targets from DrugBank that interact with the drugs in the hinted drug d φ h community C x having property φ (T φ x ), and the targets from DrugBank that interact with the drugs with property φ not included in DDSN's C x (T φ x ). 3.
For the set of tested drugs D φ t , we use molecular docking to check the interactions between all possible drug-target pairs, defined as the Cartesian product of sets D φ t and T φ (with

4.
For the set of reference drugs, we apply molecular docking on separately designed drug-target pairs for reference drugs in C x (D φ x ), and reference drugs not in C x (D φ x ) respectively, such that any drug-target pair is well-documented in the literature, and In Equations (12) and (13), Boolean function l is defined as l (i, j) = 1 if the interaction between drug d i and target t j is listed in DrugBank 0 otherwise .

Ligands and Targets Preparation
We generate all ligands' three-dimensional coordinates using the Gaussian program suite with the DFT/B3LYP/6-311G optimization procedure.

Docking Protocol
We perform the molecular docking analysis using Autodock 4.2.6 with the molecular viewer and graphical support AutoDockTools [46].
In the docking protocol, for the protein targets, we create the grid box using Autogrid 4 with 120 Å × 120 Å × 120 Å in x, y, and z directions, and 1 Å spacing from the target molecule's center. For steroidal target Ergosterol, the grid box is 30 Å × 30 Å × 30 Å in x, y, and z directions, with 0.375 Å spacing from the target molecule's center.
For the docking process, we chose the Lamarckian genetic algorithm (Genetic Algorithm combined with a local search), with a population size of 150, a maximum of 2.5 × 10 6 energy evaluations, a gene mutation rate of 0.02, and 50 runs. We adopted the default settings for the other docking parameters and performed all the calculations in vacuum conditions. We then exported all AutoDock results in the PyMOL ( We evaluate the performance of Autodock 4.2.6 by redocking and then expressing the results as root-mean-square deviation (RMSD) in Å. We perform all the calculations in duplicate and express the results as averages. The redocking involves the overlapping of the ligands for calculating the RMSD with the Discovery Studio software. We also run a comparative RMSD analysis between Autodock 4.2.6 and AutoDock Vina to assess the docking method's repeatability and reproducibility. Figure 3 illustrates the resulted DDSN, built according to our method, where the node colors identify the distinct modularity clusters.

DDSN Analysis
To mine the DDSN topological complexity, we identified the drug clusters (or communities) using both the modularity [35] and the force-directed, energy-based layout Force Atlas 2 [34] algorithms. The two clustering techniques are compatible [41]; however, the energy-based force-directed layout clustering offers more information about the relationship between clusters and acts as an efficient classifier [47]. In the case of DDSN, the clusters correspond to drug communities C x , x ∈ N * , such that V = m i=1 C x . Using the constructed DDSN from Drug Bank 4.2 and expert analysis, we label each cluster according to its dominant property (i.e., the property that better describes the majority of drugs in the cluster-see Supplementary file SupplementaryDDSN for detailed proof), which may represent a specific mechanism of pharmacologic action, a specifically targeted disease, or a targeted organ. We also confirm the clustering consistency across multiple DrugBank versions in pdf Supplementary Information, Section S2, Figure C1.
When using network clustering, if a drug does not comply with the community/cluster label, then this indicates a possible repurposing [48]. We labeled the clusters using the drug properties listed by DrugBank or reported in the literature, such that the dominant property or properties (i.e., properties found in more than 50% of the drugs in the community) give the name of the community, as indicated in Tables 1 and 2. According to Tables 1 and 2 (column Literature [%]), our DDSN computational approach recovers/reconstructs a significant number of drug repurposings reported in the literature (see the Supplementary file SupplementaryDDSN for detailed confirmation literature lists, including some recent repurposing confirmations), namely 26.98% of the 1008 drugs in DDSN (the last line in Table 2, summarizing the confirmation results).   . The drug-drug similarity network, where nodes represent drugs and links represent drug-drug similarity relationships based on drug-target interaction behavior. The layout is Force Atlas 2 [34], and the distinct node colors identify the modularity classes that define the drug clusters. We identify the 26 topological clusters with rounded rectangles and provide the functional descriptions for each of them.

Illustrative Examples of Reconstructed Drug Repositionings
Here, we present a few illustrative examples of reconstructed drug repositionings, as confirmed by recent literature. We provide the entire list of drug repositionings we recovered with the DDSN method and the references that prove them as such in the Supplementary file SupplementaryDDSN.

Reconstructed Repurposings as Antineoplastic Agents
The topological community 1 (i.e., C 1 ) consists of antineoplastic drugs, mostly mitotic inhibitors (e.g., Etoposide, Teniposide, Vincristine, Vinorelbine) and DNA-damaging anticancer drugs (e.g., Doxorubicin, Valrubicin, Mitoxantrone). This community also contains fluoroquinolone antibiotics (targeting the alpha subunits of two types of bacterial topoisomerase II enzymes, namely DNA gyrase and DNA topoisomerase 4) and a few other drugs. However, DrugBank does not confirm some drugs' anticancer effects within topological C 1 , yet the literature confirms them as such. For example, Colchicine, which is currently used based on its anti-inflammatory effects as an antigout drug, exhibits anticancer effects [49]; Podofilox, a drug for topical treatment of external genital warts, is a potent cytotoxic agent in chronic lymphocytic leukemia (CLL) [50]; for some fluoroquinolone drugs, the literature reports anticancer effects (e.g., Enoxacin [51], Ciprofloxacin [52], Moxifloxacin [53], Gatifloxacin [54]). In Figure 4, we show a zoomed detail from our DDSN, by highlighting the presence of Colchicine, Podofilox, Enoxacin, Ciprofloxacin, Moxifloxacin, Gatifloxacin in C 1 ; such topological placement suggests their antineoplastic effect.
The topological community C 6 consists of anticancer drugs that target hormone-dependent organs (i.e., ovary, endometrium, vagina, cervix, and prostate). In this community, Progesterone has the highest value of betweenness/degree ratio, and the DrugBank database does not indicate its anticancer property. Although there are extensive epidemiological studies that link the long-term Progesterone use in oral contraceptives to breast cancer risk, this link is strengthened or weakened by various parameters, such as body weight, age, duration of use [55], parity, age at first birth, breastfeeding, and age at menarche [56]. However, J.C. Leo et al. determined the whole genomic effect of Progesterone in PR-transfected MDA-MB-231 cells and found that Progesterone suppressed the expression of genes involved in cell proliferation and metastasis, concluding that Progesterone can exert a strong anticancer effect in hormone-independent breast cancer following Progesterone receptor (PR) reactivation [57]. Quinacrine is an antiprotozoal drug that exhibits an anticancer effect in breast cancer because it produces apoptosis by blocking cells in S-phase, induces DNA damage, and inhibits topoisomerase activity [58]; indeed, reference [59] recommends the clinical trial test of Quinacrine for the treatment of patients with androgen-independent prostate cancer. The antineoplastic drug Mimosine attenuates cell proliferation of prostate carcinoma cells in vitro [60]. Figure 5 provides a zoomed detail (i.e., focused view) of the DDSN that highlights Mimosine's presence (an experimental antineoplastic which inhibits DNA replication) in C 6 ; this indicates that Mimosine has effects in hormone-dependent cancers. Figure 5. Zoomed DDSN detail of community C 6 (Drugs interfering with hormone-dependent cancers). The red arrow indicates the reconstructed drug repositioning: Mimosine-an experimental antineoplastic that inhibits DNA replication-also has effects in cancers affecting hormone-dependent organs.

Reconstructed Repurposings as Anti-Inflammatory Drugs
According to the properties listed in DrugBank, the topological community C 3 includes drugs that exert anti-inflammatory effects via different mechanisms: non-steroidal anti-inflammatory drugs (e.g., Diclofenac, Ibuprofen, and Acetylsalicylic acid), the antirheumatic agent Auranofin, hypoglycemic drugs (e.g., Rosiglitazone, Troglitazone), and the antihypertensive drug Telmisartan. Moreover, the literature confirms that 28.57% of drugs within this community also present anti-inflammatory effects, even if they are not listed as anti-inflammatories in DrugBank. Here, we present the example of the versatile molecule of Fenofibrate, which reduces the systemic inflammation independent of its lipid regulation effects, with cardiovascular benefits in high-risk [61] and rheumatoid arthritis patients [62]. Another illustrative example is that of Amiloride, which inhibits the activation of the dendritic cells and ameliorates the inflammation besides its diuretic effects, thus having benefits for hypertensive patients [63]. Figure 6 shows a zoomed DDSN detail, highlighting the presence of Fenofibrate and Amiloride in C 3 ; this may indicate that the highlighted drugs also have anti-inflammatory effects.

Reconstructed Repurposings as Antifungal Drugs
The topological community C 25 includes 22 drugs. According to DrugBank, 13 out of these 22 drugs have antifungal properties, and 9 drugs act on the central nervous system (i.e., general anesthetics, sedative-hypnotics, and antiepileptics). DrugBank lists Isoflurane and Methoxyflurane as general anesthetic drugs. However, A. Giorgi et al. performed in vitro tests to investigate the antibacterial and antifungal effects of common anesthetic gases, and they found that Methoxyflurane and Isoflurane have excellent inhibitory effects on cultures of Klebsiella pneumoniae and Candida albicans [64]. Using in vitro experiments, V.M. Barodka et al. also found that Isoflurane's liquid formulation has better anti-Candida activity than the antifungal Amphotericin B [65]. Figure 7 shows a zoomed DDSN detail highlighting the presence of Isoflurane and Methoxyflurane in C 25 ; this indicates that the highlighted drugs may also have antifungal effects.

Repositioning Hints Prioritization
A high degree node represents a drug with already documented multiple properties in our characterization of drug-drug similarity networks. Furthermore, a high betweenness (i.e., the ability to connect network communities) indicates the drug's propensity for multiple pharmacological functions. By this logic, the high-betweenness, high-degree nodes may have reached their full repositioning potential, whereas the high betweenness, low degree nodes (characterized by high betweenness/degree value b d ) may indicate a significant repositioning potential. However, predicting such high-value cases of degree d, weighted degree d w , betweenness b, and betweenness/degree b d is difficult because the corresponding distributions are fat-tailed [66]. Although all the estimated DDSN centralities follow a power-law distribution (see Figure 8), the betweenness/degree b d is the most stable parameter and, hence, the most reliable indicator of multiple drug properties. To explore the capability of b d to predict the multiple drug properties, we exploit the community structure of DDSN by following a two-step approach.

1.
We uncover the relevant drug properties by generating network communities C x with x = 1, m (m = 26 in our DDSN). Then, using expert analysis, we assign a dominant property to each community. Figure 3 illustrates the 26 DDSN communities as well as their dominant functionality.
The dominant community property can be a pharmacological mechanism, a targeted disease, or a targeted organ. For instance, the community 1 (C 1 ) consists of antineoplastic drugs which act as mitotic inhibitors and DNA damaging agents; Community 13 (C 13 ) consists of cardiovascular drugs (antihypertensive, anti-arrhythmic, and anti-angina drugs), mostly beta-blockers.

2.
In each cluster C x , we identify the top t drugs according to their b d values. From these selected drugs, B t x ⊂ C x , some stand out by not sharing the community property or properties, and thus, can be repositioned as such. To this end, for x = 1, m eliminated from B t x the drugs whose repurposings were already confirmed (i.e., performed by others and found in the recent literature), thus producing m = 26 lists of repurposing hints yet to be confirmed by in silico, in vitro, and in vivo experiments, Table 3 presents the lists of B t x drugs for t = 5 and x = 26 (i.e., the top 5 b d drugs in each community). We chose t = 5 to provide a reasonable amount of eloquent information in Table 3; we provide the entire B x sets in the Supplementary file SupplementaryDDSN.
To facilitate the visual identification of the repositioning hints, in Figure 9, we shape the size of the nodes of our DDSN representation according to the magnitude of the b d values. By arrows, we also identify the top b d nodes (i.e., drugs) in their respective communities, by indicating their community id. Table 3  The high percentage of database and literature confirmations of our pharmacological properties predictions highlight the robustness of our repurposing method. In the Supplementary file SupplementaryDDSN, we show that the confirmation rate ∑ x B c x / ∑ x C x = 86.51%. Table 3 presents a similar situation, with only a few unconfirmed drug properties (these repurposing hints ∈ B h x are in bold).  Figure 9). Meprobamate is a hypnotic, sedative, and mild muscle-relaxing drug, with no reported activities on the antifungal drug targets; thus, the antifungal activities of Meprobamate are not yet investigated in silico (with molecular docking), in vitro, or in vivo. Acarbose is a hypoglycemic drug, with no reported nor investigated antiarrhythmic and anticonvulsant properties.
At the same time, one should also consider repurposing hints for drugs with high b d , when the highest b d values correspond to drugs already confirmed with the community property. For example, Azelaic acid has the highest b d across not confirmed drugs in C 6 .

Repurposing Hints Testing
Molecular docking uses the target and ligand structures to predict the lead compound or repurpose drugs for different therapeutic purposes. The molecular docking tools predict the binding affinities, the preferred poses, and the ligand-receptor complex's interactions with minimum free energy. In this paper, we use the AutoDock 4.2.6 software suite [46], which consists of automated docking tools for predicting the binding of small ligands (i.e., drugs) to a macromolecule with an established 3D structure (i.e., target). The AutoDock semi-empirical free energy force field predicts the binding energy by considering complex energetic evaluations of bound and unbound forms of the ligand and the target, as well as an estimate of the conformational entropy lost upon binding.
According to the methodology in Section 2 (Section 2.3), we verify the predicted properties of repurposing hints by performing molecular docking not only for the hinted drugs but also for the reference drugs (typical drugs having the predicted property) and for some drugs with little probability of having the expected property. This way, we facilitate the comparison between the interaction of the hinted drug with the biological targets-relevant for the tested property-and the interactions of the reference drugs with the same targets.
Following the methodology in Section 2 (Section 2.3), we first consider the property φ as the anticancer effect with x = 6 (corresponding to community C 6 ), and second φ as the antifungal effect with x = 25 (community C 25 ). As such, we test the repurposing hints D  Figure 10 shows the summary of interactions resulted from the molecular docking analysis of the drug-target pairs generated with Equations (11)-(13) (Section 2, Section 2.3.1) for the hint D anticancer h = {Azelaic acid}. For the hint and the reference drugs D anticancer r , we represent the interactions with the targets T anticancer as the number of amino acids from the target interacting with the drug molecule (the maximum is 21). We provide the details related to the molecular docking simulations in the pdf Supplementary Information-Tables S1-S6 and Figures S1-S6. Figure 11 presents the summary of interactions resulted from the molecular docking analysis of the drug-target pairs generated with Equations (11)-(13) (see Section 2, Section 2. After Autodock 4.2.6 and AutoDock Vina redocking according to the procedure in Section 2.3.3, we calculate RMSD in both cases. We obtain low RMSD values (i.e., all of them are ≤ 1.016 Å), suggesting that our preliminary docking methodology is robust [68] (details in SuplementaryInformation.pdf file, Section S6).

Discussion
Drug repurposing represents a promising strategy to accelerate drug discovery in sensitive areas of nowadays medicine, such as antibacterial resistance, complex life-threatening diseases (e.g., cancer), or rare diseases. In this paper, we describe a novel weighted drug-drug similarity network whose weights encode the existing known relationships among drugs (i.e., quantifies the number of biological targets shared by two drugs irrespective of the agonist or antagonist effect).
We then demonstrate that the ratio between node betweenness and node degree (i.e., a criterion of combined network metrics) can indicate the drug repositioning candidates better than considering simple network metrics (e.g., degree, weighted degree, betweenness). Indeed, the power-law distributions in Figure 8 suggest that our DDSN is a complex system; thus, the conventional statistical analysis of the DDSN can be misleading. Consequently, we introduce a different approach to deciphering the emerging hidden higher-order functional interactions (i.e., interactions that span multiple orders of magnitude and involve multiple nodes) by visualizing and analyzing the community structure in DDSN and determining the culprits (for such unknown functionalities) through combined network metrics criterion. We use the force-directed energy layout Force Atlas 2 to generate network clusters of drugs [34] because it emulates the emerging processes of a complex system. More precisely, the force-directed based network layouts use micro-scale interactions (i.e., adjacent nodes attract and non-adjacent nodes repulse) to generate an emergent behavior at the macro-scale (i.e., topological clusters). Once we identify communities, the combined network metrics criterion selects the drug repositioning most likely candidates. Specifically, our weighted drug-drug network analysis encodes not only information about how pairs of drugs interact with biological targets but also reveals the unknown functional relationship between drugs, such as the unknown effects on the activation/inhibition of a chemical pathway or cellular behavior. We used a similar methodology-underpinned by force-directed layout clustering-to analyze the fundamentally different structures represented by the drug-drug interaction networks (i.e., the DDIN interactome [48,69]).

Complex Network Perspective
When analyzing networks built with drug data, one must be aware and carefully deal with data incompleteness. Mestres et al. acknowledged this problem for networks built with data from the 2006 DrugBank version, where drug-target data scarcity was indeed a problem [70]. However, in this paper, we worked on a much more comprehensive database, with a much larger and denser number of nodes/drugs and connections. Still, even if recent years' research alleviated the data scarcity problem, any network analysis has to consider a degree of entailed uncertainty.
Another important aspect of our method's data processing is the interpretation of b/d ranking. We chose this composite centrality because its distribution in DDSN is more stable than other centralities; therefore, as also suggested by [71,72], it should produce more robust rankings. However, reliable confirmation of b/d as an efficient priority indicator requires retrospective in vivo, in vitro, and in silico (i.e., molecular docking) experiments, and we encourage future research in this way.
We select Azelaic acid (saturated dicarboxylic acid) and Meprobamate (carbamate derivative) as possible antineoplastic and antifungal from our repurposing hints list, respectively. Even so, one may find a posteriori confirmation clues for such repositioning hints. For instance, in [73], the authors discuss the antitumoral effects of Azelaic acid in the case of melanoma and only hypothesize that it may be tested in hormone-related cancers. Furthermore, the Meprobamate molecule contains a moiety that can be associated with antifungal effects [74]. However, these associations only make sense because our DDSN analysis orients this process. Moreover, in the docking experiments, the two hints are not structurally similar to the respective reference drugs (i.e., Progesterone and Abiraterone for antineoplastic, and Clotrimazole, Oxiconazole, Naftifine, Tolnaftate, Nystatin, Natamycin, Ciclopirox, Griseofulvin for antifungal). Indeed, Progesterone and Abiraterone are steroid derivatives, Clotrimazole and Oxiconazole are imidazole derivatives, Ergosterol has a steroidal structure, Terbinafine and Naftifine are allylamine compounds, Griseofulvin is a 3-coumaranone derivative.

Molecular Docking Perspective
Molecular docking represents an alternative, in silico simulation approach to drug discovery, which models the physical interaction between a ligand (i.e., small drug molecule) and a macromolecule (e.g., synthetic host macromolecule, biological target) [75]; it is also a valuable repurposing tool [68,76]. We estimate the free energy values of the molecular interactions with molecular docking to offer a good approximation for the ligand's conformation and orientation into the protein cavity [77]. DOCK [78] is a dedicated software tool used in drug repurposing along with many available molecular docking models. For example, R. L. Des Jarlais et al. used the Dock computer algorithm to find that haloperidol inhibits HIV-1 and HIV-2 proteases [79]. However, molecular docking can not work unless we have some strong repositioning hints; otherwise, the search space for drug repositionings would be exponentially big. To this end, the methodology proposed in this paper provides strong drug-target interaction hints, such that we can build large-scale drug-target interaction profiles [8,80]. Our approach integrates the molecular docking with complex networks to hint new pharmacological properties by identifying new sets of biological targets on which the drug acts. However, in this paper, we performed only a preliminary docking testing, as our primary focus is the network-based repurposing approach. As such, we recommend that future, more focused, research continue our docking simulations by including target baits (to reflect the limitations of false-positive and false-negative results), considering solvent effects, flexible docking, and comparing multiple docking tools. To this end, we indicate the robust docking methodologies employed in [68,[81][82][83].
As Yvonne Martin et al. indicated [84], the paradigm of chemical similarity-which holds that structurally similar drug molecules exert similar biological effects-cannot fully explain drugs' biological behavior. They found that only 30% of compounds similar to a particular active compound are themselves active (the compounds are structurally similar if the Tanimoto coefficient is ≥0.85 in the Daylight fingerprints). Therefore, behavioral approaches can successfully complement the structural paradigm. To this end, similar interaction profiles are valuable resources in drug repurposing, as drugs with similar target binding patterns may exhibit a similar pharmacologic activity [80,85,86]. As the chemical similarity is not necessarily a reliable predictor of biological similarity [84,87], we analyze the binding modes of Azelaic acid and Meprobamate compared to the other known reference drugs (see Sections S3-S5 in the pdf Supplementary Information).
We highlight the docking simulation results for the interaction between Azelaic acid and Steroid 17-alpha-hydroxylase/17,20 lyase, highly similar to Progesterone and Abiraterone interactions with this target (see pdf Supplementary Information, Table S4). Abiraterone is a potent 17-alpha-hydroxylase/17,20-lyase inhibitor used for the treatment of androgen-dependent prostate cancer [37]. Therefore, discovering new drugs that inhibit this enzyme is a logical strategy. However, because steroidal drugs-such as Abiraterone-have multiple steroid-related side effects, Hille et al. decided to synthesize non-steroidal compounds that mimic the natural 17-alpha-hydroxylase/17,20-lyase substrates (i.e., pregnenolone and progesterone) [88]. Our docking simulation results are in line with references [89,90], which report the covalent bonding of Abiraterone to Steroid 17-alpha-hydroxylase/17,20 lyase (a cysteinato-heme enzyme from the cytochrome P450 superfamily). Precisely, Abiraterone forms a coordinate covalent bond of the pyridine nitrogen at C17 with this target's heme iron [90]. Furthermore, our docking simulation of the interaction between Abiraterone and 17-alpha-hydroxylase/17,20-lyase confirms that Abiraterone establishes a hydrogen-bond between the -OH group and the target's Asn202; our results also confirm that amino acid residues of Phe114, Ile206, Leu209, Arg239, Gly301, and Val482 represent the hydrophobic environment for the reference Abiraterone [91]. According to our docking simulation results, Azelaic acid does not establish a hydrogen bond with Asn202; however, not all the inhibitors tested by Chun-Zhi Ai et al. form a hydrogen bond with Asn202. (Instead, they bond to other amino acid residues than Abiraterone [91].) In a recent paper, Gabriele Micheletti et al. reported results of biological and docking evaluations of some hybrid aza-heterocycles compounds, which bound azelayl moiety through an amide bond that act as histone deacetylase inhibitors; this suggests the anticancer potential for three of their Azelaic acid derivatives in osteosarcoma among the five tumor cell lines tested [92].
Meprobamate has similar binding modes to that of Clotrimazole with Lanosterol 14 alpha-demethylase, Oxiconazole with Lanosterol synthase, and Griseofulvin with Tubulin. Indeed, we find the carbamate moiety in a wide range of drugs, such as Felbamate (anticonvulsant), Disulfiram (the treatment of chronic alcoholism), Rivastigmine (anti-dementia), Darunavir (antiviral for the treatment of HIV infections), or Physostigmine (antiglaucoma). Furthermore, carbamates are reversible acetylcholinesterase inhibitors that act as effective fungicides, insecticides, and herbicides in agriculture [74]. Indeed, a recent reference reports the synthesis, in vitro, and in vivo antifungal evaluation of 36 novel threoninamide carbamate derivatives using the pharmacophore model [93].

Conclusions
The overarching conclusion is that our network-based computational drug repurposing method is robust, as it recovers a wide array of previous drug repositionings. We prove such robustness by employing our approach on an older database, to validate the results with a new DrugBank version. Nonetheless, in drug repositioning, we deal with unknown unknowns; thus, we need to consider the seemingly unconfirmed drug properties as potential repurposing hints. Testing all these hints is a daunting task that requires vast resources; thus, we propose a testing prioritization method based on network centralities.
In this paper, we started a preliminary validation of previously unaccounted drug properties using molecular docking. As such, we find that the Azelaic acid represents a promising candidate for further in silico (e.g., molecular dynamics), in vitro, and in vivo investigations of its potential anticancer effects. Although the molecular docking results are not as strong as for Azelaic acid, Meprobamate's antifungal properties cannot be disregarded or rejected. Meprobamate is a known oral drug; however, we cannot exclude the topical administration route as an antifungal. To this end, we need further investigations on biopharmaceutical properties to test various pharmaceutical topical formulations with Meprobamate as an active ingredient. The same discussion on the biopharmaceutical properties is valid for Azelaic acid, knowing that its administration route may change as an anticancer drug.
Our findings pave the way for further employing the target-based drug-drug similarity networks with the latest available drug-target interaction data, as well as for in vitro and in silico experiments that will eventually establish useful drug repositionings.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript:

DDIN
Drug-Drug Interaction Network DDSN Drug-Drug Similarity Network FDA U.S. Food and Drug Administration NDA New Drug Applications NME New Molecular Entities