The Review of Ecological Network Indicators in Graph Theory Context: 2014-2019

Ecological Network Analysis (ENA) capability has led to develop a set of indicators. Ecological Network Indicators (ENIs) investigates a range of subject in different context “e.g. Graph theory”, which is the origin of variety of questions such as following: What is the geographical distribution of studies and their relationship with each other? On what elds these studies are focused? What graph-based index or indexes have been used in the studies of ecological networks? What are the most widely used indexes in ecological studies? Accordingly, this study is to investigate the related literature between 2014 and 2019 in the framework of graph theory. To answer the mentioned question, we conducted systematic literature review. To nd as many potentially eligible articles as possible, the search was performed multiple times using diverse related keywords. We identied 456 related records. After the screening process, 114 articles were left as the basis of further analysis. The results indicate that ENA applied mainly in China, USA, France. ENIs is studied more frequently among plants and mammals. We identied about 58 ENIs. But the Probability of Connectivity (PC), Integral index of connectivity (IIC) have been consistently used in most studies. Also, these two indices are used in combination with others ENIs. The outcomes show researchers introduce new indexes every year. The increasing trend of introducing new indicators shows the usability and applicability ENIs. But so far, PC, IIC, and LCP seem to be the most credible graph-based indexes for use in ecological network research. The overall results imply that graph theory as base of ecological network is developing, presents new indicators and opening new dimensions in the study and analysis of connections and communications in ecological networks. It has adequate exibility to answer questions that may arise in the future in the eld of ecological network analysis.

and methods that have been presented in this eld recently are updated to be. The authors reviewed the indicators used in such studies, which were published between 2014 and 2019. For achievement to the main aim, the following research questions are speci cally 2. B) Selecting the keywords of the search as follows: "Graph Theory", "Ecological Networks", "Fragmentation", "Landscape Connectivity", "Landscape Ecology", "Urban Landscape", and any combination of these terms.
The searched databases were Google Scholar and ISI Web of Knowledge. This search was narrowed to articles written in English in which graph theory has been used in the study of ecological networks.
To nd as many potentially eligible articles as possible, the search was performed multiple times, each time with the term "Graph Theory" used as the xed keyword but combined with one of the following complementary terms: "Ecological networks", "Fragmentation", "Landscape connectivity", "Landscape ecology", "Urban landscape". Finally, the search results were sorted in the descending order of the publication year (from 2019 to 2014).

Selection Process
The eligible articles were selected through the three-phase process used by Mehring et al. (2019). The diagram of this process is illustrated in Figure (1). In the rst phase, articles that had the term "graph theory" and one of the complementary keywords ("Ecological Networks", "Fragmentation", "Landscape Connectivity", "Landscape Ecology", "Urban Landscape") in their titles, abstracts, or keywords were listed (duplicate articles were discarded). The number of articles in this phase was 456. After sorting the articles in the order of their publication year, in the second phase, the texts of the articles were examined to be clear whether the articles in the text also deal with graph theory or not? and those articles that were not related to the eld of interest and those that had not used graph theory were discarded. This was done to enhance the focus in selecting articles on the subject under study and avoiding mistakes. Because in some researches, although keywords are included in the title, abstract and keywords, they are not used in the research text. Bringing these researches in the results and analysis causes an error in the research and diverts it from the main goal. Eventually, A total of 167 scienti c articles were found to meet these criteria. In the third phase, the articles that had not used the graph-based indexes were discarded, leaving 114 articles. These 114 articles had used graph-based indexes for ecological analysis.

Analysis
The grounded theory (GT) was used to reach a simpler and more organized categorization of indexes used in the articles so that the results can be presented and discussed in separate segments. This method involves systematic data collection followed by systematic analysis and simpli cation of the collected contents (Glaser & Strauss, 2017). The core idea of this method is to gather data about a speci c subject through research and then transform the gathered data into concepts and categories through repeated comparison and re nement (X. Li, Du, & Long, 2019). In this study, the software VOS viewer was used for data visualization where needed.
In the analysis of articles, the following were investigated: geographical distribution of studies by country and continent, employed indexes, main indexes, number and composition of employed indexes, novel indexes, ecosystem composition of the use of graph-based indexes, frequency of use of graph-based indexes by the number and type of species, frequency of use of graph-based indexes in different elds of ecology. Although, The relationship between the indicators is investigated using Spearman correlation.

Geographical Distribution of Studies
The use of the graph-based approach in ecological research does not have an even geographical distribution. This approach has been used most frequently in Europe and Asia, followed by North America. Only a limited number of studies in other regions have used this approach.
The results show that the studies using this approach have been limited to 26 countries (Fig. 2). China (16.67%), the USA (13.15%), and France (13.15%) have the highest number of studies. Other countries with a notable number of studies are Spain (6.14%) and Australia and Canada (5.3%). Also, 4.38% of the studies have not been focused on any speci c country.
The results also show that researchers from 37 countries have taken part in the reviewed studies. The highest rates of participation are related to researchers from the United States, France, and China with 27%, 20%, and 19%, respectively.
Ecosystem Composition of The Use of Graph-based Indexes in The Field of Ecology Ecological indexes can be used in the analyses of all types of ecosystems. But as expected, these indexes were mostly used in the study of terrestrial ecosystems (80%). In 15.65% of the reviewed studies, indexes were used to study aquatic ecosystems. The rest of the studies (4.35%) were not focused on any speci c ecosystem (Fig. 3).

Indexes
In the 114 reviewed studies, a total of 58 indexes were used 160 times. In these studies, the indexes were used in two ways: 1individually, 2-combined with other indexes. In terms of frequency of use, some indexes were used for many years, but some others were new and had not been used as frequently. Therefore, this issue was taken into account during the analysis.

Frequency of Use of Graph-based Indexes by the Number and Type of Species
The 114 reviewed studies were categorized from two perspectives: 1-the number of species studied, 2-the type of species studied.
Approximately 85.09% of the studies were performed on one species, 6.14% were performed on two species, 4.38% were performed on 3 species, and 0.88% were performed on 5 species. The remaining 3.51% of the studies were general. Table 1 shows the number of singlespecies studies that were conducted on each type of species. Table 2 shows the number of studies performed on two, three, and ve of each type of species.

Name and Usage Frequency of Employed Indexes
The frequency analysis showed that the studies had used the graph-based indexes 160 times. In terms of frequency of use, the indexes were divided into three categories: 1) widely used, 2) intermittently used, and 3) rarely used. The indexes PC ( (Table 4, Table 5).    Table 3.

Statistical relationships between Indexes
In order to explore the relationship between the indexes, the Pearson correlation is conducted. Because the main indexes frequency was less than two, any statistical analysis was meaningless. Therefore, the correlation was calculated for indexes with equal or more than 2 frequency. As result in Table 6 shows: no speci c relationship is considerable. Only a weak and negative relationship is observed between PC and LCP (-0.335). The second meaningful relation is observed between the AWF and F index. Table 7 depicts the signi cance level alpha.

Discussion
The last decade has seen the growing importance of research into ecological networks, and therefore, the tools used in such research.

Geographical Distribution of the Studies
The examination of the geographical distribution of the use of graph theory in the eld of ecology showed that the method is more widely in Europe and North America and also more evenly used across these continents. In Asia, this method has not been commonly used anywhere outside China, which has the world's highest number of studies with this approach (19 studies). What is interesting about these results is the higher concentration of studies conducted in the developed countries, which can be attributed to the higher priority given to ecological sustainability.
These studies have been conducted to examine the extent of habitat communication as well as animal communication, so this indicates that the critical areas in this regard are African, Asian and South America countries. The importance of South America and Africa in biodiversity, as well as the lack of studies on these continents, is a wake-up call for researchers, politicians and the public. Given that in these areas, animal habitats are disappearing one after another, so these results can draw the attention of o cials in these countries for more policy and investment on conservation and environmental connectivity, and Also attract the use of new scienti c methods in this eld.

Species studied
Species diversity in research using graph theory in ecological network analysis is a positive point in the e ciency of graph theory in studies on different species. However, there are some points in the results that need further analysis, for example, graph theory has been used for different species, but the results show a high difference in the frequency of study of the studied species. Which we will discuss in the following.
In the three main categories that were done, most of the graph theory was used for animal species with 79 uses, followed by plants with 37 uses and then litter with 15 uses. The low frequency of studies on the Context in ecological elds and its high difference with the other two categories raised the question of whether graph theory is effective in the study of context connections. Looking at the issues that have been done in these studies, it has been observed that studies in the eld of bedding are divided into four categories: water network connections, roads, residential structure and land uses. Studies on connections on water networks are more prominent than other cases that have been studied in various forms such as delta, wetland, river networks. As Na Xiu and colleagues suggest, Only a small number of studies have provided speci c approaches or suggestions in geographical distributions (Xiu et al., 2017). Therefore, in the future, researchers can use the capabilities of graph theory in the eld of context study or further study the challenges of graph theory in this eld.
Animal species have the most use of graph theory so that out of 131 cases studied, 79 cases have been assigned to them. However, it cannot be said that all animals have a relatively similar pattern of movement or share common factors. After classifying animals in groups that have a relatively similar pattern of behavior, it has been observed that the focus of further studies is on mammals, birds, reptiles and amphibians. In the meantime, aquatic animals and insects were each in the margins with 5 frequencies compared to other animal species. Due to the speci c characteristics of aquatic animals and insects, there are reasons such as di cult to track, lack of access to the minimum required information, etc., and this may indicate that these species are not attractive to researchers. Given the diversity of species and the importance of aquatic animals and insects, it is hoped that in the future more researchers will use graph theory in the analysis of the ecological network of these two species.

Indexes Employed Indexes
In the reviewed studies, 58 graph-based indexes have been used 160 times in ecological network analyses. The results show that the indexes PC, IIC, and LCP have the highest frequency of use in these studies. PC, IIC, and LCP can be considered the most popular indexes for research in the eld of ecology. It should be noted that the less frequent use of other indexes is not because of their ineffectiveness, but rather because many of them have been introduced more recently and it will take some time for them to become widely recognized and established. Nevertheless, the frequent use of PC, IIC, and LCP suggests that these three indexes can be trusted to yield fairly reliable results in ecological analyses. There are also a small number of old indexes that have not been used as frequently, which indicates that they have not been accepted by the scienti c community.
One of the bene ts of using graph theory in ecological analyses is that graph-based indexes can be used in combination with each other to study multiple aspects of an ecological network simultaneously. Out of the 114 studies reviewed in this work, 23 had used two indexes. Of these 23 studies, 9 had used a combination of PC and IIC. This shows that these two indexes can be used together in research in the eld of ecological network analysis.
The studies were also examined from the perspective of the composition of species studied. This examination showed that 85.09% of the studies were focused on a single species. Also, 6.14% of the studies (7 studies) were focused on two species. Among these 7 studies, two studies were focused on mammal and reptile-amphibian species ( interesting point regarding LCP, however, is its frequent use in the analysis of connectivity for reptile-amphibian species with frequency 4, which shows the suitability of this index rather than IIC for use in this particular eld. In comparison to IIC and PC, LCP has a wider area of application.
Other Indexes ECA has a usage frequency of 2.5% and has been used in 4 of the reviewed studies, of which three studies have been on animal species and one on plant species. LSP has been used 3 times in the studies on mammal, reptile-amphibian, bird, and plant species. NC has also been used 3 times, in two studies on plants and one study on animals. MGP, NL, AWF, F, and SP have each been used in two studies. For MGP and NL, both studies have been on plant species, for F and SP, the studies have been on mammals and context, and for AWF the studies have been on plant and mammal species. The remaining 47 have each been used in only one study. Among these indexes, SPT and EC have each been used in three areas, RNG, VIF, MSSN, and CI have each been used in two areas, and other indexes have been used in one area. The species for which graph-based indexes have been used least frequently are aquatic species with 5 instances and insect species with 6 instances, and the species for which these indexes have been used most frequently are mammal species and plant species with 58 and 53 instances, respectively.

Indexes Similarity and Correlation
The similarities of indexes and correlation between index could appear the cluster of related indexes. As Table 6 and 7 depicts, there is no considerable relationship between the indexes. While a variety of indexes is used, but no speci c concentration is observed on a group of indexes. It means that although, some indexes such as PC, IIC and LCP have a relatively high frequency, but the collection of ecological networks is under evolving. Therefore, we face a collection of indexes which is applied in different domains. Consequently, no main core of indexes is shaped. Another reason is related to the different context that ecological networks are applying. The wide domain of use and indexes diversity lead to shape any core indexes.
Despite less statistical similarities, the PC, IIC and LCP have main used indexes. Moreover, the used indicators could be classi ed into three categories: rst those indicators which is used lonely (frequency = 83). This group includes 72.81% of the studies that have used only one index; second, 20.17% of studies have used two indexes (frequency = 23); third, a combination of more than 2 indicators (frequency = 8). In the Last group, 3.51% used three indexes ( Table 6). The highest number of indexes used in a study is ve, which has occurred in only 1.75% of the studies.
As mentioned, the indexes most commonly used in the studies are PC and IIC with usage frequency of 29.81% and 18.63%, respectively. The results show that in 8.77% of the studies, PC has been used in combination with other indexes. For IIC, this gure is 7.02%. This shows the popularity of combining PC and IIC with other indexes. Considering the years in which these indexes have been used in combination with others, it can be concluded that they have not lost their analytical value over time.    In this regard, the results show that graph-based indexes have been used more frequently in terrestrial ecosystems. Naturally, this could be due to higher accessibility of terrestrial ecosystems, availability of data, ease of observation, and ease of access to target species in these ecosystems.
It was found that although a large portion of studies has been performed on only one species, graph theory is exible enough to be used in the analysis of ecological connectivity and connections in multiple species. For example, in a 2016 study by Naicker et al., this approach was used to study ve species.
The results also showed that most studies have been focused on animal species. Plant species and context are next in this ranking. Also, four of the studies have been general. These results demonstrate the wide applicability of graph theory in a wide variety of ecological network analyses. However, it should be noted that apparently this approach is mostly used for terrestrial plants and mammals.
Nevertheless, given the exibility of this approach, one can expect that it will be used more frequently and in a wider variety of applications. For example, in a 2019 study by Mestre in Iberia, context and landscape fragmentation were analyzed by considering roads and linear infrastructure as links and residential areas as nodes. In another example, Niculae et al. (2017) attempted to use a graphbased approach to investigate the spread of invasive species. This shows that graph theory can be used not only in ecological network analyses aimed at increasing connectivity but also in ecological network analyses with the purpose of decreasing connectivity or other aspects of ecological connections when necessary. Therefore, graph theory can be expected to nd wider application in ecological research, including in the spread analysis of viruses and infectious diseases.

Future directions
In research, the use of graph theory in the eld of ecological network connection focuses on ecological connections. Important issues that can be discussed in relation to the future of graph theory in ecological network analysis are geographical distribution and diversity in analysis approaches.
Given that the number of countries in which studies have been conducted is increasing every year. It is promising for researchers to use and familiarize themselves more with the application of graph theory in the eld of ecological network analysis. The results showed that from 2014 to early 2019, the number of countries in which studies were conducted has increased. During this period, as shown in Fig. 4, 15 countries were added to the countries in which the studies were conducted. Continents of great ecological importance, such as South America with a frequency of 2 cases and Africa with a frequency of 2 cases, are very few in these new studies, while they can use the capacity of graph theory in ecological network analysis according to Problems in these continents that bene t greatly from the fragmentation or loss of ecological habitat. However, the results show that there are two points that new countries will join in the future.
And the trend will be upward but not too fast and familiarity with this graph theory in ecological network analysis will have an upward trend with a low slope.
The diversity of the studied species is very high, but the point that is very important and should be considered is that the basis of graph theory is the analysis of the ecological network in its raw form, which can be used to both reduce and improve Ecological network used. So far, most studies have been done to protect or improve the ecological network of the species. While the high potential of chart theory can be used in areas that require ecological disconnection to study species that need to be disconnected, such as pest species, invasive species, or diseases with Viral origin. Therefore, it is predicted that in the future, the use of Kraft theory in the eld of reducing ecological network communications will increase due to its necessity and play a more prominent role in this eld.

Conclusions
In this study, the past studies that have used graph theory in the analyses of ecological networks were reviewed. In general, it was found that the graph theory is exible enough for the analysis of different ecological networks and has been extensively used in recent years to study and analyze ecological connections and connectivity in different ecosystems and a wide variety of species. For these reasons, graph theory is useful in the analysis of the ecological network of habitat networks. Therefore, in the future, this approach can be expected to be used more widely in the area of ecological network analysis.
One of the features of the use of graph theory in ecological network analyses is the continuous emergence of novel indexes, as every year researchers develop several new graph-based indexes for use in these analyses. Therefore, one can conclude that graph theory has enough exibility to answer questions that may arise in the future in the eld of ecological network analysis.
Although researchers are introducing novel graph-based indexes for ecological network analyses every year, the credibility of many of these indexes will be determined in time by whether they will be effectively used in future researches. But so far, PC, IIC, and LCP seem to be the most credible graph-based indexes for use in ecological network research.
There are many advantages to the use of graph theory in ecological network analysis as it has low information requirements and can be used in research on different species. Therefore, researchers need to direct more attention and effort to the development and adaptation of this theory for use in ecological network analyses. It is hoped and expected that researchers will make further use of this theory in the analyses of ecological networks, expand it for use on different aspects of connectivity in different species, and use it to develop more accurate and useful tools and indexes for these analyses. Availability of data and materials The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.