Bats and rodents are hosts of a significant proportion of zoonoses, higher than any other mammalian order. Over 200 viruses belonging to 27 viral families have been isolated or detected in bats; however, bat-human transmission has only been observed for 11 viruses, belonging to four different viral families: Rhabdoviridae, Filoviridae, Coronaviridae and Paramyxoviridae (Allocati et al., 2016) . Some examples of those viruses are as follows: SARS-related coronavirus, Sosuga rubulavirus, Ebola virus and Marburg virus, rabies lyssavirus, Nipah henipavirus and Hendra henipavirus (Allocati et al., 2016; Calisher, Childs, Field, Holmes, & Schountz, 2006; Hayman, 2016; O'Shea et al., 2014; Plowright et al., 2015) .
Rodents have similar zoonotic potential to bats and are associated with a large number of zoonotic viruses, such as Sin Nombre virus, Puumala virus, Crimean-Congo hemorrhagic fever virus, Kyasanur forest virus, tick-borne encephalitis virus, Lassa fever virus and Venezuelan equine encephalitis virus, among others. All of the aforementioned bat-and rodent-associated viruses have a large impact on public health. However, it is important to take into count that not all of these viruses are obligate pathogens; some are generally commensal.
Previous studies have explored viral associations on relatively restricted spatial or phylogenetic scales. For example, Hayman (2016) propose maps of viral distributions according to the distribution of hosts' families, Streicker et al. (2010) explored rabies viruses using a phylogenetic approach, and Cui, Tachedjian, and Wang (2015) compared retrovirus associations between bats and rodents. Anthony et al. (2017) explored coronavirus networks at the level of host family, and Bordes, Caron, Blasdell, Garine-Wichatitsky, and Morand (2017) analyse the relationships among zoonotic diseases in Southeast Asia. Luis et al. (2015) analyse viral networks between rodents and bats at global scale identifying several ecology factors to explain virus-host associations. Recently, works explored the specificity and frequency of sharing DNA and RNA viruses among Carnivores and bats (Wells, Morand, Wardeh, & Baylis, 2018) and the importance of the phylogeny to explain the viral richness associated with bats and rodents (Guy, Thiagavel, Mideo, & Ratcliffe, 2019) . However, there are currently no studies at a global level that incorporate the human influence in the viral networks.
While some authors consider bats and rodents to belong to a similar category of high zoonotic risk potential (Han, Schmidt, Bowden, & Drake, 2015) , other work examines the differences between bats and rodents (Luis et al., 2015) . Several different distinctive features of bats have been hypothesized to explain their particularly high viral richness, such as their ability to fly, long migrations, high trophic diversity and social structure (Brook & Dobson, 2015; Moratelli & Calisher, 2015) . However, currently the viral diversity and connectivity among different species of bats are not well understood (Moratelli & Calisher, 2015; O'Shea et al., 2014) (Luis et al., 2013) . Rodents, like bats, have been recognized as reservoirs for several zoonotic viruses (Han et al., 2015) , such as virus of hantaviridae (Schmaljohn & Hjelle, 1997) and arenaviridae families (Charrel & de Lamballerie, 2010) . However, there are differences in rodent-virus associations that impact their zoonotic potential compared with bats.
In disease ecology, analytical tools have been used to holistically explain the dynamics of infections and provide novel hypothesis to explain macroecological patterns (Johnson, Roode, & Fenton, 2016) . One of the theories that helps to predict dynamic changes in host-pathogen systems is graph theory, also known as network theory (Bordes et al., 2017; Johnson et al., 2016) . This approach can be used to gain better understanding of how interactions take place within pathogen communities, how hosts are connected with pathogens, their preferred association and patterns of pathogen transmission (Godfrey, 2013; White, Forester, & Craft, 2017 ).
The graphs, better known as networks, focus on the interactions between entities (Newman, 2014) , and they have the potential to infer relationships within a larger framework (Hossain & Feng, 2016; Luke & Stamatakis, 2012) . A network is capable of emphasizing the preferred union as a process (Hartonen & Annila, 2011) and capturing both the individual elements in a system as well as their relevant interconnections (Kolaczyk & Csardi, 2014) . In disease ecology, this kind of analysis could be applied to describe viral diversity associated with different hosts and detect hosts and viruses that share associations, and therefore identify groups that share similar characteristics (White et al., 2017) .
In network theory, centrality and dispersion metrics quantify the importance of each component member (Martínez-López, Perez, & Sánchez-Vizcaíno, 2009; Newman, 2014; Opsahl, Agneessens, & Skvoretz, 2010) . The parameter "betweenness" can be used to Impacts • The analysis of virus and host networks (rodents and bats) allows us to measure the potential risk of zoonotic diseases.
• Measuring network connectivity can be a useful tool for identifying hosts and viruses of potential importance in the transmission dynamic of zoonotic diseases.
• Bats presented twice as many connections between virus and host as rodents, indicating a higher zoonotic potential transmission.
recognize dispersing hosts and key viruses in the evolution or viral transmission (Opsahl et al., 2010; White et al., 2017) , while "closeness" can indicate hosts and viruses that may have little direct connectivity but are surrounded by important highly connected nodes (Opsahl et al., 2010; White et al., 2017) . In terms of disease ecology, we can employ these and other parameters to explore the host-host, virus-host and virus-virus interactions by collapsing the networks and identifying communities. Network analysis thus offers the opportunity to recognize highly diverse viruses and hosts based on a high degree of connectedness. Bats and rodents are excellent taxa in which to implement this tool because they harbour a large number of highly adaptable viruses and hosts with high resistance. Therefore, in this study we aimed to compare and recognize the differences in the associative capacity of the host-virus networks in rodents and bats worldwide, as well as to identify the viruses that may shift across species, including humans, suggesting zoonotic potential. does not exist in the ICTV classification, we assigned all reports from Astroviridae family as astrovirus. To increase the certainty of identification of the viruses, only studies that used molecular methods to detect viruses were included in the database we compiled.
Subsequently, each of the viruses identified in rodents or bats was classified as direct zoonotic or non-zoonotic pathogens (Allocati et al., 2016; Calisher et al., 2006; Han et al., 2015) .
An independent undirected bipartite network was built for each of the orders of Rodentia and Chiroptera. That is to say, each network included two types of nodes-viruses and hosts. Viral nodes were connected to host nodes when the virus indicated by the node has been detected in the species indicated by the host node. We included a human host node, which was connected to viruses that have been classified as zoonotic. This helped us to group and identify zoonotic viruses and viruses close to them (which could have zoonotic potential).
Then, host-to-host and virus-to-virus networks were constructed in order to explore these networks in different dimensions. The "bipartite.projection" function in the igraph package implemented in r software version 3.4.2 (R Core Team, 2017) was used to collapse the bipartite network. Basically, in the collapsed networks a host was connected to another host when they shared a common virus and a virus to a virus when they shared a common host ( Figure 1 ).
In each host-host collapsed network, the host nodes were conserved and the virus nodes were transformed using the weight of corresponding links in order to illustrate the relationships among different hosts (Figure 1a ,b). In each virus-virus network (one for bats and one for rodents), the virus-virus relationship was highlighted by collapsing the host nodes into the weighted links ( Figure 1c ).
We measured the networks on two levels: individual node and the entire network. At the node level, we measured different centrality values including: degree (number of links that a node has), betweenness (number of times a node is an intermediary to connect each possible pair of nodes) and closeness (the degrees of average separation in relation to other nodes) (Martínez-López et al., 2009; Newman, 2014) . At the network level, we measured density and diameter. Network density is the proportion of links that are actually observed in the network divided by those that could possibly occur and network diameter is the length of the longest geodesic distance (Newman, 2014) .
Network level measurements were useful for summarizing the "big picture" of the network and identify the key nodes that are closely related to humans. Network level measurements were generated using the algorithms provided in the packages "igraph" (Csárdi Table 1 ), and plots were produced using the packages "igraph" and "ggplot2" (Gómez-Rubio, 2017) in r (R Development Core Team, 2011).
Communities were detected using the Maximization of Modularity method (Newman, 2016) , which recognize nodes with dense and weak connections between groups. We used the function "cluster_ edge_betweenness" (Girvan, Girvan, Newman, & Newman, 2002; Newman & Girvan, 2003) in the "igraph" package (Csárdi & Nepusz, 2006) to identify the nodes with dense connections with humans, which is based on the following equation:
where m denotes the total number of links in the network, A ij refers to the actual number of links between nodes i and node j , γ is a parameter calculated by the algorithm; K, degree of i; δ gigj is a randomized number of links between a pair of nodes. Community detection facilitates the recognition of groups of hosts that share viruses and viruses that share hosts, and which therefore may continue to enter in contact with each other because they share similar characteristics.
A subnetwork was built by choosing communities with more than four host-virus pairs, which is above the minimum number accepted in statistical normality samples (n = 3) (Hammer, Harper, & Ryan, 2001; Royston, 1982) . These subnetworks were illustrated to gain better community visualization and recognize the most relevant communities for the detection of potentially zoonotic viruses.
From the subnetwork, the most important communities were chosen using to the measures of the members (top five nodes) and the number of zoonotic viruses (80%) as selection criteria. Then, a sociogram representing the preferential unions and the complex interaction on the largest communities was constructed using the package "visnetwork" (Almende, Thieurmel, & Robert, 2016) in r. This choice of subnetworks helps us to focus and observe in more detail the interactions within these important communities.
The rodent database contained 825 records including 172 rodent species and 123 viruses, of which 53 are zoonotic viruses. The bat database contained 4,659 records, consisting of 220 bats species associated with 166 viruses, of which 40 viruses were classified as zoonotic. Both databases are detailed in Appendix S1. Table 2 , and centrality values are in Appendix S2. 78.06% of the nodes had a degree value of 1 or 2, making them uninformative in terms of epidemiological information, though they may be involved in co-evolutionary processes.
Thirty-nine different communities were detected. Sixteen communities included only two members, while the largest group consisted of 32 members. This particular group included humans, as shown in Appendix S2.
Ten communities with at least eight members were selected in the subnetwork (Figure 2b ). We excluded communities 1 and 9 despite fulfilling the inclusion criteria because they are linear, with a single virus that influences the whole.
(1)
TA B L E 1 Formulas applied to calculate networks parameters
Degree centrality (D)
Freeman (1978) Closeness centrality (C) 
This network contained 147 nodes of rodent species with 502 links.
The diameter of the network was 5, and the density was 0.0627 ( Figure 3a) . The top five nodes in terms of degree, betweenness and closeness are shown in Table 2 , and the remaining values are in Appendix S3. Thirty-five different communities were detected, and the largest of which contained 43 members, followed by a group of 21 members (Appendix S3). 
A total of 387 nodes (220 bat species, 166 viruses, human node) and 736 links were contained in the bipartite bat network. The network diameter was 10, and the density was 0.0049 ( Figure 4a ). Three zoonotic viruses had the highest degree and betweenness values;
these were bat coronavirus, rabies lyssavirus and bat paramyxovirus (Table 4 ). 65.71% of the nodes had degrees of 1 or 2, so they do not provide much information to the network but they may be involved in co-evolutionary processes. All centrality values are given in Appendix S2.
Twenty-nine different communities were detected; four of those had only two members, and the largest community contained 38 members (Appendix S2). 
Eleven communities contained eight or more members (Figure 4b ).
Communities 1, 3 and 4 were linear and possessed simple edges, with a virus that influenced the whole community. Community 7 was a homogeneous community with rich ecological interactions, but which was not highly related to zoonotic viruses. The last community was associated with humans had the highest number of zoonotic viruses involved (Figure 4c ,d, details below).
A low number of zoonotic viruses were found in homogeneous bat network communities. We focused only on the community that included the human node. In Figure 4a , three red lines representing the three highly connected viruses in the network followed by a homogeneous community and later in green the human node connections.
The community that included humans (Figure 4c ,d) has 13 host nodes (including human) and 23 virus nodes with 45 links. Fruit bat parvovirus was the only non-zoonotic virus in that community.
Miniopterus, Mormopterus and Saccolaimus were the only bat genera that directly shared viruses with humans.
The host-host Chiroptera network contained 221 nodes and 6,949
links. The diameter and density of the network were 5 and 0.2911, respectively ( Figure 5a ). The five nodes with the highest centrality values are shown in Table 5 , and detailed results are in Appendix S4.
Sixty-seven different communities were detected; the largest had 69 members. The second largest community consisted of 56 members including humans (Appendix S4).
The virus-virus network contained 164 nodes and 2,132 links.
The diameter of the network was 4, and the density was 0.1655 
Bats are well-known as excellent reservoirs for zoonotic viruses that usually result in high public health impact (Gay et al., 2014; Luis et al., 2013 Luis et al., , 2015 Plowright et al., 2015) . Nevertheless, in our database, (Tables 3 and 5 ). However, the clusters in the bat network are four times denser compared with rodents; this makes it easier to continue sharing the viruses. In addition, they can act as virus mixers, allowing the viruses to acquire characteristics that allow them to infect other host species, including humans. In addition, the human node is more closely connected to bats. It shows that viruses are shared to a greater degree among bats as discussed earlier (Figures 3a and 5a) . One plausible explanation is that many species of bats live in high-density populations, with many individuals in close proximity to each other, such as in caves and roosts sites.
Indeed, there are always a larger number of bat species than rodent species in a given area (Kerth, Perony, & Schweitzer, 2011) .
The difference in connectivity between the bat and rodent hostvirus networks has implications for the zoonotic potential of each taxon. High connectivity facilitates viral transmission within and between species, and so, bats are expected to have higher zoonotic po- For that reason, deeper comprehension is required to unravel this entanglement.
One of the objectives covered in this work was to recognize non-zoonotic viruses that may be strongly connected with humans and therefore have zoonotic potential. The bat-virus community that contained humans was composed of bats distributed in Africa and Australia may be explained by high rates of human-bat contact (Allocati et al., 2016; Rupprecht, 2009 ).
One non-zoonotic virus that was included in the bat-virus community that included humans is fruit bat parvovirus. The parvoviridae family were transmitted from bats to other mammals by a viral ancestor suggesting their zoonotic capacity, and groups of genes in their genome denote this potential (Canuti et al., 2011) . Even though the virus currently infects only bats (Canuti et al., 2011) , it is firmly connected with the human node in our network by Pteropus poliocephalus, a species endemic to Eastern Australia (Lunney, Richards, & Dickman, 2008) . Future studies are recommended to elucidate its potential for zoonosis.
Andes viruses (rodents), cowpox (rodents) and rabies lyssavirus (bats) were defined as main actors (high values of degree, betweenness and closeness) in the bipartite networks. However, their importance disappeared when the network was collapsed to virus-virus interactions, likely because their geographical restriction may limit their viral connectivity. Andes virus is only distributed in South America (Martinez et al., 2005) , cowpox in Europe (Vorou, Papavassiliou, & Pierroutsakos, 2008) and rabies lyssavirus in America (Moratelli & Calisher, 2015) . Therefore, these viruses In the rodent community selected, community 3 has members with predominantly European distribution. Further, two non-zoonotic viruses are included among the nine zoonotic viruses, but we do not think they are likely to have zoonotic potential because they do not have direct contact with the human node. Therefore, in this community we do not find viruses with zoonotic potential.
In the rodent community 5, M. musculus has high values of connectivity but in the sociogram (Figure 2d) , it is evident that the connectivity is with non-zoonotic viruses. This host species thus is likely less important in public health terms, but highly relevant for disease ecology. In addition, two zoonotic viruses are included in the community 5, and while they can transfer their zoonotic potential to other non-zoonotic viruses using M. musculus as a virus mixer, we consider this unlikely because the proportion of zoonotic viruses is low, adding the specificity of rodents' viruses and the associative characteristics founding in the rodents. Thus, the one-to-one virushost species relationship suggested by the node-to-edge ratio suggests that spillover is unlikely, though not impossible.
In the human-rodent community, Gbagroube virus is noteworthy because it is the only non-zoonotic virus found in the community. Gbagroube virus should be closely monitored along with its host, Mus setulosus, found in Central Africa (Granjon, 2016) .
In our study, the human is the most relevant and largest node connected in both groups. The relevance of the human in the network is explained by several factors. First, humans' enormous population and globalization push human populations to nearly everywhere on earth and greatly increases the probability of contact with innumerable organisms, resulting in the emergence of zoonotic diseases (Kock, 2014) . Secondly, because zoonotic diseases have clear social implications, once detected in one species, they are much more likely to be tested for, and thus detected, in others (Oliver-Morales & Abarca García, 2016). It is therefore possible that the high apparent importance of humans in the networks is more due to the over-representation of zoonotic viruses in the literature than to humans actually being particularly highly.
In the database, we do not have Ebola virus reports because in the database the DBATVIR database did not identify the host species from which the virus was isolated. Similarly, we found that 78.06% of rodent nodes and 65.71% of bats nodes were poorly connected (1-2 degree). Surely, bats have associations that we do not recognize. In addition, there are associations that could occur but do not, but these cannot be identified because cases in which viruses were tested for and not detected are not often reported. We therefore think it is important to report negative samples and the number of animals tested in meticulous reports.
A future study may complement and compare our study with models where the influence of humans is omitted. We must take into account that the human node influences the network structure, and the ecological relationships must be analysed without this influence.
Surely, laxer networks will be observed when the connective force of humans is removed. However, our study does need to include both to identify potentially zoonotic viruses.
It is pertinent that, in future investigations, different characteristics of the viruses must be considered simultaneously and not only by their connectivity in the network such as gene sequence, type of transmission and virulence. In the present study, we focus only on viral host capability, not on the symbionts and their associative nature. Spatial analysis may help to further explain how our findings apply among different regions of the world.
Graph theory, beyond allowing the visualization of complex interactions, allows the quantification of many aspects of connectivity and structure.
Rodents should be taken into account as important reservoirs for zoonotic viruses, since in our database, a greater proportion of the total viruses reported were zoonotic viruses in rodents than in bats. Fruit bat parvovirus in bats and Gbagroube virus in rodents should be monitored to elucidate their zoonotic potential. In the present study, we only assessed their network proximity to humans and other zoonotic viruses, and molecular genetic approaches may help to confirm our results. Counting the number of zoonotic symbionts associated with each order is not a conclusive estimate of their zoonotic potential. Our findings reveal that viruses were more frequently shared among bats than rodents. For that reason, bats have more zoonotic potential that the rodents. However, potential emerging zoonotic diseases may arise from both taxonomic groups.
We are very grateful to PAPIIT (Project IA206416), Programa Castillo for their contribution in the construction of the databases.
We declare that we have no conflict of interest.
Gerardo Suzán https://orcid.org/0000-0002-9840-2360
Oscar Rico-Chávez https://orcid.org/0000-0002-9833-1101