Mapping (mis)alignment within a collaborative network using homophily metrics

Collaborative approaches can overcome fragmentation by fostering consensus and connecting stakeholders who prioritize similar activities. This makes them a promising approach for complex, systemic problems such as lack of reliable, safe water, sanitation, and hygiene (WASH) services in low-income countries. Despite the touted ability of collaborative approaches to align priorities, there remains no comprehensive way to measure and map alignment within a network of actors. Methodological limitations have led to inconsistent guidance on if, and how much, alignment is needed around a common vision (e.g., universal, reliable access to WASH) and/or around an agreed set of activities (e.g. passing a bill to promote water scheme maintenance models). In this work, we first define alignment as the extent to which actors work with others who share priorities. We then develop and test a method that uses social network analysis and qualitative interview data to quantify and visualize alignment within a network. By investigating how alignment of two strong, well-functioning WASH collaborative approaches evolved over three years, we showed that while alignment on a common vision may be a defining aspect of collaborative approaches, some alignment around specific activities is also required. Collaborative approaches that had sub-groups of members that all prioritized the same activities and worked together were able to make significant progress on those activities, such as drafting and passing a county-wide water bill or constructing a controversial fecal sludge disposal site. Despite strong sub-group formation, networks still had an overall tendency for actors to work with actors with different prioritized activities. While this reinforces some existing knowledge about collaborative work, it also clarifies inconsistencies in theory on collaborative approaches, calls into question key aspects of network literature, and expands methodological capabilities.


Introduction
In a collaborative approach, all relevant stakeholders discuss, plan, and carry out a set of agreed activities to reach a shared vision [1]. When that shared vision requires broader systems

Literature review
In the international development sector, collaborative approaches are seen as a "highly effective means to scale and sustain impact through increased alignment and coordination between stakeholders" [14] (p. 18). This makes them a promising approach for complex, systemic problems such as lack of reliable, safe WASH services in low-income countries, and, as a result, they are increasingly implemented in the WASH sector. Yet, despite a wealth of practical knowledge and a growing body of literature on collaborative approaches in WASH (see Pugel et al. [2]), existing guidance has not investigated alignment. Our study starts to address this gap by drawing from the literature on collaborative approaches and network theory, and then applying it to cases in the WASH sector.
When it comes to alignment, the literature on collaborative approaches and network theory are limited in four important ways. First, literature on collaborative approaches cite the importance of alignment but cannot agree on its granularity, i.e. whether alignment is needed on visions and/or activities. Second, network analysis techniques have sought to map alignment but have only mapped priorities and relationships separately, not together. Third, network literature seeks to measure network strength but does not consider alignment, in part due to the aforementioned methodological limitations. Fourth, homophily analysis has been widely used to map the extent to which actors with similar attributes are working together, but has only PLOS WATER been used to assess quantitative, objective attributes, rather than qualitative, subjective attributes such as priorities. These limitations are described in more detail below.

Review of collaborative approaches and alignment
Collaborative approaches convene a group of diverse stakeholders to collectively accomplish shared, complex visions that cannot be solved by any single entity working alone. The process they follow largely entails the facilitation of a collaborative group to agree on a vision (e.g. universal access to water services in a district) and activities to implement to achieve the vision (e.g. establishing and regulating a private maintenance service provider). Collaborative approaches then encourage stakeholders to coordinate and work together to implement agreed activities, sometimes requiring a change to their own organizational agendas. Members must dedicate some of their own time, and sometimes resources, to implement these activities. Literature studying collaborative approaches have noted the importance of alignment as an outcome [15,16] but has not clearly defined what it means. For instance, the collective impact framework claim a key outcome is that actors are "implementing aligned action" [3]. Collaborative governance literature has cited an outcome as being actors "carry[ing] out actions. . . that align with the intentions of the [collaborative group]" [16] or the extent to which there is a "mutual alignment of agendas" [17]. Communication scholars define the idea of "co-orientation" as "a process whereby people align their actions in relation to common objectives through an ongoing dialectic of conversations and texts" [18, as cited in 19]. Loosely, literature on collaborative approaches uses the term to mean the process of actors working together with the same intentions. We build off these key concepts for this work, defining alignment as the extent to which actors work with others who share a common objective.
Objectives of members have largely been broken down into two key areas: a vision and activities that could reach that vision. Different activities are different "means to an end", with the "end" being the common vision. Vision alignment would therefore mean that actors who agree on the common vision are working with one another, while activity alignment would mean actors work with others who agree on a common set of activities. Yet, existing theory on inter-organizational collaboration, ironically, disagrees on the extent of alignment that is needed. Some guidance [1,20] cites the importance of vision alignment, while other sources [3,21] argue for activity alignment. In practice, it is more challenging to achieve activity alignment as it requires more time, resources, and occasionally, conflict resolution and facilitation skills. This is especially true in the WASH sector, in which almost all stakeholders are in some way working towards the vision of improved access, reliability, and sustainability of services, but many actors seek to reach this vision through different activities. Thus it is important to have guidance on how much alignment is necessary for collaborative approaches, as well as how the process of alignment occurs.

Review of networks and alignment
Mapping alignment requires an understanding of both the relationships between stakeholders as well as each stakeholder's priorities. Network analysis is a popular technique used to systematically map relationships of stakeholders, typically referred to as "actors" [22], making it wellsuited for understanding alignment. In the WASH sector, network analysis is increasingly used by organizations and by facilitators of collaborative approaches to better understand stakeholders and relationships [23][24][25].
A few network researchers have made significant strides in trying to study alignment using network analysis, but all are limited in significant ways. Largely, existing work has analyzed actor perceptions of alignment rather than collecting data on actual priorities and real relationships. For instance, Nowell [13] used network analysis to analyze ties of "shared philosophy", signifying which actors are perceived by others to "share a similar philosophy about the collaborative's targeted issue and how it should be addressed" (p. 199). The study found that perceptions of alignment, meaning shared "beliefs and understandings about the issue", was important for meaningful change [13]. However, modeling peer's perceptions of alignment, rather than whether the actor's priorities are aligned or not, limits the study. Ogada et al. [10] looked at perceived alignment as an attribute of actors in a network analysis study and found that actors with higher interest in the group's vision had higher perceived influence in the network, finding that stakeholders "who know and astutely exploit their interests and sphere of influence are more effective participants" in a collaborative approach (p. 287). This is supported by findings from Kolleck et al. [11], who investigated predictors of 'common vision identification' within Collective Impact networks and found that members more central to the network had higher identification with the groups' visions. While these two studies made strides to investigate alignment, they focused on the extent to which individuals identified with the network's vision, without dissecting the different individual priorities of actors. Walters et al. [12,26] overcame these limitations by cross-tabulating each individual actor's values and perceived influence to investigate conflict and power within a network, making them the first to map alignment of actors' prioritized values, rather than perceived alignment. Yet, they did not investigate actor relationships in addition to their objectives, though this was suggested in the study as a needed area of future work. Thus, as current methods stand, there remains no way to measure or quantify the extent to which actors work with others that share their priorities.

Review of network strength and alignment
By mapping all relationships between actors, network analysis can investigate where relationships occur, where they do not, and "the implications of both for achieving outcomes" [27]. Network researchers have sought to measure networks by their 'strength' to find metrics that can predict what influences the ability of the network to accomplish those outcomes, including their "ability of a group to coordinate" [28] or their ability to be "connected in ways that facilitate achievement of a common goal" [27]. Largely, these studies focus on strength metrics that investigate the structure of the network, such as number of connections [28], strength of connections [13], reciprocation of connections [29], and knowledge about the network structure [30,31]. However, the literature on collaborative approaches has recommended investigating process-oriented aspects of network strength [32,33], which could include relationships amongst those with shared priorities.
Investigating alignment as a strength metric would also respond to calls from communication scholars who argue that structure-oriented research largely misses much of the important processes that are central to collaborative work [32,34]. A well-tested metric for alignment could be used to measure and, in turn, comprehensively investigate the process of alignment.

Review of homophily metrics and alignment
One promising network analysis technique has high potential as a way to map alignment: homophily, meaning the tendency for similar actors to be connected [33]. This method has been around for many years, allowing network researchers to investigate "both the attributes of actors and relations among them. . .. [to explain] of how and why they decide to cooperate with each other" [35]. Homophily analysis investigates the tendency of actors to connect to other actors with similar attributes/ characteristics, including socioeconomic characteristics [33], sub-group membership [36], geographical locations and culture [37], political affiliation [38], and demographics such as race, gender, or culture [39]. Homophily analyses typically focus on categorical attributes. Those that focus on quantitative network parameters, for example the node degree or total number of connections a node has to others in the network [40], are referred to as assortativity analyses [41]. However, some studies have inconsistently also used assortativity calculations for categorical attributes [42,43], meaning the terms are somewhat interchangeable. Despite the overlap, we will refer to it as homophily analysis.
A central focus of homophily analyses is understanding whether, and how much, actors in a network tend to connect to similar actors, i.e. those with the same attribute, compared to different actors, i.e. those with different attributes. Largely, many have found that actors with similar attributes are more likely to be tied together. Shrestha and Feiock [39] explain this phenomenon through transaction costs, where creating ties with similar actors has lower transaction costs than creating ties with dissimilar actors. They illuminate this further: "It is easier for a local jurisdiction to bargain and negotiate with other jurisdictions when they have a similar demographic composition, because their preferences and motives are likely to be similar. . .. [and] increases the likelihood of collaborative relationships" (p. 14, emphasis added). They assume that similarities in demographics and socioeconomic characteristics translates directly to also mean similar ideas and priorities for actions or activities.
Arguably, this "birds of a feather flock together" theory makes sense logically, where actors with similar priorities, objectives, and motives face lower transaction costs of implementing activities if they work together. However, these assumptions may not hold when looking at collaborative networks that convene actors with diverse priorities [44]. For instance, Ogada et al. [10] conducted a homophily analysis within a collaborative network to investigate if actors tend to connect to similar institution types (e.g. government agencies with government agencies). They found that actors tended to collaborate with different types of institutions (e.g. government ministries with local water user associations) because each type of actor brought different strengths to the table. While Ogada et al.'s study [10] laid important groundwork for investigating alignment, they only looked at homophily by actor type, not by actor priorities. This reveals a gap, where no homophily studies have comprehensively investigated the extent to which a strong, collaborative network is comprised of actors working with those with similar priorities. Greater research is thus needed to understand the extent to which like-minded actors work together in collaborative approaches, and homophily analysis is a promising technique to do so.

Research questions
As described in the literature review, clear gaps remain in the literature on collaborative approaches and networks. These gaps stem from two highly related limitations: first, there is no comprehensive way to measure alignment, and second, due to the lack of methods, alignment has not been comprehensively investigated over time in strong, well-functioning collaborative approaches. To address these gaps, this study focused on two research questions: (a) How can alignment be measured? (b) How do actors in strong collaborative networks align over time?

Methodology
Alignment was modeled using five steps (Fig 1): network construction, prioritized activity identification, attribute assignment, homophily analysis of dyadic connections, then repeating the process over time. To test the method, we investigated alignment of two collaborative networks in the WASH sector over three years. Network analysis terminology refers to people or organizations as 'nodes' and the relationships between them as 'ties'. The mapping and calculations are typically conducted using computer software such as UCINET, gephi, kumu, NodeXL, and R [45]. Before detailing these steps, it is important to explain the cases included in the study.

Ethics statement
Research methods were reviewed by the University of Colorado Institutional Review Board under protocol number 17-0292 and 18-0314 and was deemed exempt as the participants responded on behalf of their organization or agency.

Cases in context
This study was conducted as a part of the U.S. Agency for International Development (USAID) Sustainable WASH Systems Learning Partnership (SWS), which is a five-year program seeking to learn about the actors and factors driving WASH systems strengthening. This study investigated alignment of two collaborative groups at different snapshots in time: one at three snapshots in time and the second at two snapshots in time. In total, five networks were analyzed. These two cases were selected for their high data quality and for the demonstrated achievements that the collaboratives were able to achieve. Both cases had an agreed-upon common vision that they worked towards, with one seeking to strengthen town-level sanitation in Ethiopia and the other aiming to improve sustainability of rural water services in a county in Kenya.
3.2.1. Debre Birhan Learning Alliance. The Debre Birhan Learning Alliance was a newly formed network in September 2018, with many of the members not coordinating much before the group formed. With support from Tetra Tech and SWS, the network formed and identified their common vision as strengthening sanitation services in the town. Comprised of 20 to 25 actors, largely town-level government officials, service providers, community representatives, and other non-government entities, the network met quarterly to identify ways to strengthen their town's sanitation. One of the network's key accomplishments was being able to engage all relevant actors, secure funding, and construct a temporary fecal sludge dumping facility in 2020. In addition, they also increased sanitation allocations in the municipal budget over time. Interview data for the network relationships and priorities was collected at three points in time: 2018, 2019, and 2020.

Kitui WASH Forum.
The Kitui WASH Forum has been a coordination platform since 2016. They share a common vision of all citizens in the county having reliable access to water. In 2018, SWS partners (Unicef Kenya, Oxford, and Rural Focus Ltd) strengthened the existing network to be more action-oriented with the vision of finding ways to improve WASH in the county together. More than fifty actors attend any single quarterly meeting, but just over twenty actors represent the central group of regular attendees. A key accomplishment of the network was drafting the first a County Water Bill to provide an enabling environment for universal water service access by addressing core sector issues such as monitoring,

PLOS WATER
Mapping (mis)alignment within a collaborative network using homophily metrics coordination, funding, professionalization of rural water management, among others. This bill is not yet enacted but is under review by the county parliament. This network has interview data on priorities and relationships in the network from two points in time, 2018 and 2020.

Step 1. Network construction
To construct each network (Step 1), all members of the collaborative group were asked to indicate the extent to which they connect with every other actor in the group [45]. In line with McPherson et al. [33], who argues that different relationship types should be compared in the homophily analysis, we investigated multiple relationship types. Relationship types included information sharing and support. Information sharing includes face to face meetings, phone calls, emails, and any other method of providing information outside of the formal reports and general presentations to groups of people. Reports and presentations were not included because then all actors in the network would have this relationship, as they all attend regular quarterly meetings together. Support indicates working together on water or sanitation issues, specifically who they give support to or receive support from (training, equipment, permits, studies). Relationship strength was not included in this analysis; relationships were either present or absent. This data was collected with closed-ended questionnaires as is typical for network analysis data collection techniques [45]. Questionnaires were conducted by experienced enumerators hired locally, who collected answers verbally in the national local language or in English, as appropriate, and entered by the enumerator into a form on a portable tablet. All work met all ethics standards and was reviewed by University of Colorado Institutional Review Board under Protocol #17-0292. Informed consent was obtained orally, which is justified because the research posed minimal risk of harm to subjects, as it asked about relationships and perspectives of the respondent's organization not their individual self.

Step 2. Activity prioritization
To determine actors' prioritized activities (Step 2), semi-structured interviews were conducted at the same time as the SNA interviews. Semi-structured interviews asked each actor about (1) the biggest problems facing water or sanitation services in their district or town, (2) activities that would solve those problems, and (3) the activity their organization saw as the most important. Rather than only asking respondents about their prioritized activities, this series of questions related to problems, activities, and priorities, giving more depth and validation to responses. Interviews were translated, transcribed, and qualitatively coded by the research team to establish a list of priorities emergently using either QSR NVivo 1 or Dedoose1. We used two different qualitative coding softwares in order to match the software used by the partner organization. Using grounded theory techniques commonly used throughout qualitative coding methods [46], the list of activities was revisited and synthesized so that the final list only included five prioritized activities for each network, for ease of comparison across time. Five total activities showed to sufficiently capture the variation in perspectives while also allowing similar activities to be grouped together. With greater than five attributes, the visualizations became too cluttered to interpret, while with fewer, they were too simplified and did not capture sufficient variation. This total number could vary in future studies and is recommended to be adjusted by the investigator to be consistent with case context.

Step 3. Activity assignment
This analysis required a single prioritized activity to be assigned to each actor, as homophily analysis only calculates a coefficient based on a single attribute. Once a list of activities was established, we returned to each interview and determined the activity deemed to be most important to that actor, in response to a question of "which of the activities listed is the most important?". On a limited number of occasions, when the question of importance was not asked (due to interviewer error) or not answered (due to interviewee vagueness), the activity listed first was identified as their priority. Prioritized activities were then assigned to actors (Step 3) by adding the activity next to their name in the node list.

Step 4. Homophily analysis
To analyze homophily of dyadic connections (Step 4), we imported relationship data from Step 1 and attribute data from Step 3 into R software. All R code for network manipulations and calculations, as well as redacted data files, are provided in S1 Text. Using the package igraph [47], we converted the data into a network object to be used for visualization and network metrics. Then, homophily parameters were used to measure the tendency of actors to connect with others that share priorities. The igraph package provides a suite of "assortativity" functions, which measure the level of homophily within the network on a scale of -1 to 1 [47]. We used the assortativity_nominal function for this analysis because it treats attributes as categorical rather than values. Other SNA software use an External-Internal Index calculation to measure homophily which uses a simpler calculation of subtracting ties between similar actors from ties between different actors and dividing by the total number of ties [48]. While the External-Internal index is a useful comparison technique, it is not able to consider 'random' tie formation, which in this case would be if an actor were to connect to another unbeknownst of their prioritized activity and that actor happened to prioritize the same activity.
The assortativity function can analyze directed networks, where a tie (e) between actor with attribute a and actor with attribute b has a direction (e a,b ). For this calculation, any actor that does not have attribute a is denoted as having attribute b. The general notation for directed ties is that the sending actor is the tail of the tie, while the receiving actor is the head of the tie (e.g. tail ! head). The assortativity function compares the fraction of ties that have tail and head a (e a,a ) to the total fraction that involve a, meaning that the tie could have tail or head a and connect to any actor a or b (i.e. e a,a , e a,b , e b,a ). The latter represents the likelihood of tie assignments based solely on proportions of ties, i.e. random assignment without any preference for the attribute of the actors. Using Eq 1, which is similar to a Pearson correlation coefficient, it then correlates the fraction of ties involving actors with attribute a (i.e. e a,a , e a,b , e b,a ) with fraction of ties connecting two actors with attribute a (e a,a ). Through this correlation it quantifies r, which is the tendency for actors to connect to similar actors. Assortativity is calculated through the following equation [49]: where e a;a is the fraction of ties with head and tail a; x a is the fraction of ties with tail a y a is the fraction of ties with head a: ½Eq1� This is similar to other homophily calculation functions in other SNA programs, thus we will refer to all assortativity coefficients as homophily coefficients, or r, for simplicity.

Step 5. Assessment of change over time
Even though relationship and priority data were collected from all network actors in each time step (2018, 2019, and 2020), the network itself changed over time, with some actors leaving and new actors joining, and priorities changing over time. For consistency of the comparison, we analyzed the actors who were interviewed at all time steps. For the Kitui WASH Forum, 22 actors of the roughly 50-actor network had both relationship and prioritized activity interview data for 2018 and 2020. For the Debre Birhan Learning Alliance, 9 actors of the 25-actor network had data from 2018, 2019, and 2020.

Explanation of homophily values
Positive values from 0 to 1 mean that actors tend to connect with other actors that prioritize the same activity, while negative values from -1 to 0 mean that actors instead tend to connect with other actors that have a different prioritized activity. A homophily coefficient of 1 means that every tie that exists in the network ties two actors with the same prioritized activity. This "convergence" of priorities is demonstrated by the mock network structures in Fig 2, in which actors are noted by dots, priorities denoted by the dot color, and connections between them shown as lines. A homophily coefficient of 1 could indicate either that every actor has the same prioritized activity (Fig 2A) or that the network is entirely fragmented and though multiple priorities exist in the network, each actor is only tied to actors with the same prioritized activity (Fig 2B).
A homophily coefficient of 0 would mean that the tendency for actors connect with similar actors is the same as a random graph, for example if actors formed ties independently of others' priorities. A homophily coefficient of -1 indicates a negative correlation, in which every tie that exists in the network ties two actors with different priorities. This could exist if every actor had different priorities or if actors that shared priorities did not have a tie (Fig 3).
Because collaborative approaches rely on multiple actors working collaboratively toward multiple activities that support one another, we hypothesize that neither a score of 1 or -1 would be beneficial for networks to work together efficiently and effectively toward a common vision.
We hypothesize that homophily coefficients that fall between 0 and 1, where actors strategically form ties connect with others that prioritize the same activity, would best enable a group to work together towards a common vision (Fig 4). This would fall in line with most literature on homophily analyses as described in section 2.4 in the literature review.

PLOS WATER
Mapping (mis)alignment within a collaborative network using homophily metrics For example, actors with different priorities could be split into multiple sub-teams that can each work on a shared priority, with a few actors that act as coordinators between groups, as is recommended by some collective approaches. Some ties would be between sub-groups as

PLOS WATER
actors worked with and provided feedback across sub-team boundaries to keep progress aimed at the overarching vision, then the network structure would reflect that in Fig 4. The homophily coefficient of this would be positive and between 0 and 1, where most ties tend to connect actors with similar prioritized activities but there are still ties connecting subgroups. If the group had a set of dedicated individuals independent of the group that coordinated across subgroups such as a "backbone" [1] or "hub" [50], then the network structure might have a set of actors in the middle that would facilitate the connections between sub-teams.

Results
First, we provide a descriptive analysis of how prioritized activities changed over time, before presenting results from the homophily analysis. Standard descriptive statistics of the networks, which are typically provided in network analysis studies but were too lengthy to include in the article body, are provided in S1 Text.

Prioritized activity frequency analysis
Despite each network being aligned around a common vision, there was a variety of activities that network members prioritized in seeking to reach that vision. In Table 1 we break down the frequency of those prioritized activities over time, tracking which activities were the most predominant in the network and how prioritized activities changed over time. We then discuss key events that may have played a role in changing priorities, first in Debre Birhan and then in Kitui. Awareness of citizens Training and raising awareness of the society at large about the proper ways to dispose of waste and empty latrines.

Commitment by town administration
Lead agencies should prioritize sanitation activities, which requires raising their awareness of the issues and their importance. Kitui WASH Forum Reliable water service delivery for the county

Professionalization of scheme management
Coordination of actors to standardize how schemes are managed and monitored, including establishing the water bill and water policy. Prefers management of schemes in a professional, coordinated wayshifting away from community management of schemes.

-6
Community management Capacity building of community management of schemes, strengthening their connection to the subcounties so they are more accountable, and strengthening ownership of schemes by communities.

-10
Infrastructure development Constructing new schemes in undeveloped areas or upgrading schemes to solar power.

-2
Qualified maintenance technicians The subcounties have skilled technicians, funds, staff, and capacity to maintain schemes.

-3
Adequate budget County and subcounty governments having access to funding and enough budget to carry out their activities.

Debre Birhan Learning Alliance.
In Debre Birhan, the network gradually started to prioritize the construction of a fecal sludge disposal site, with only two of the nine actors prioritizing it in 2018, three in 2019, and five in 2020.
Increased prioritization of the fecal sludge disposal site was a result of a few important events. Stakeholder discussion on the reports of comprehensive city-wide sanitation assessment revealed that 80% of the town's fecal waste was reaching the groundwater and nearby stream because of unsafe disposal practices, largely driven by the lack of a disposal site. Importantly, the Learning Alliance themselves decided that a fecal sludge disposal site would be a priority activity for the group and assigned members to a Task Team to specifically work on this activity. The Learning Alliance members visited the fecal sludge disposal sites of the country's capital, Addis Ababa, in 2019 as well as a town of similar size to Debre Birhan (Hawasa) in 2020. The learning visits exposed them to fecal sludge management approaches in the country and gave them ideas for some of the design. Ultimately, the Debre Birhan Learning Alliance was able to construct a temporary fecal sludge disposal site in 2020.
A separate study investigated some of the key factors contributing this progress of the Debre Birhan Learning Alliance, finding key drivers to be their method of working closely with the Town Administration to secure their buy-in as well as to access funding from private factories and town water utility for construction of FSD site facilities (access road and trench ponds for FS disposal), the collaborative way in which the alliance decided on the fecal sludge dumping site as a focus area, the strong convening power and capacity of the Municipality and Water Utility and Municipality who took over leadership of the alliance, and the ability of the alliance to establish a continuous and accountable membership [2].

Kitui WASH Forum.
The Kitui WASH Forum tells a different story, however. In 2018, the majority of the network prioritized either professionalization of scheme management (9), or community management (8). By 2020, the predominant network priority was community management (10), followed by professionalization of scheme management (6). It is important to note that the top two priorities, community management and professionalized management, are not entirely compatible. Community management has long been the norm in how schemes have been managed, which has been widely found to not provide the amount of support necessary to keep schemes functioning reliably. Thus, recent efforts have sought to require better service quality for the way schemes are managed, with professionalized maintenance being a promising option in which public or private service providers are responsible and accountable for keeping schemes functioning. Despite this apparent fragmentation, with most (17 in 2018 and 16 in 2020) actors prioritizing conflicting solutions, the Kitui WASH Forum actors were still able to draft a Water Policy which embraces professionalized maintenance models and establishes service quality standards in the County, while also providing the funding, coordination, monitoring, and contracting mechanisms to do so.
The separate study that investigated factors contributing to the Kitui WASH Forum's progress found that progress was enabled by key government officials supporting the effort and taking on key leadership roles in the Forum itself, as well as the availability of external funds to support policy development [2].
Looking at frequencies of priorities only shows one of the two critical parts of alignment (priorities and relationships). To understand alignment, it is important to overlay this analysis of priorities with the relationships between the actors who share priorities.

Homophily analysis of priorities
The homophily analysis is comprised of both calculations and network visualizations. Together, these two techniques provide deep insights into the ways in which actors with similar priorities are connected. While the homophily calculation is useful in showing overall network trends, visualizations add significant value because they can reveal how sub-groups of actors with shared priorities are connected to each other. These results will focus on different aspects of each case to highlight the varied use of the homophily analysis and visualizations. We first use the 2018 Kitui WASH Forum network to demonstrate how a positive homophily score manifests in a network. We also use the Kitui WASH Forum to show the importance of both (a) looking across different relationship types and (b) investigating sub-groups. For the Debre Birhan Learning Alliance, we focus on investigating change over time.
4.2.1. Kitui WASH Forum. The 2018 Kitui WASH Forum had a positive homophily score (r = +0.07, Fig 5) within its support network, indicating a slight tendency for actors to work with others that shared their priorities. This is compared to a negative homophily score (r = -0.02) in its information-sharing network, meaning that those same actors had a slight tendency to share information with actors with different priorities. The visualization of the support network clearly shows two distinct sub-groups, or groups of actors with the same priorities, who have many ties to one another (Fig 5). These sub-groups comprise actors who prioritize Professionalized Maintenance (PM) and those that prioritize Community-Based Management (CBM).
Visually, it is notable that the PM sub-group has more ties connecting the sub-group compared to the CBM sub-group. Actors in the PM sub-group are also more experienced and senior actors, including two from the county government who hold decent decision-making

PLOS WATER
power and influence. This contrasts with the CBM subgroup which only included one influential decision-maker from the county government. This network as a whole made significant progress from 2018 to 2020 on standardizing Professionalized Maintenance models through the development and passing of a County-wide Water Bill. This may suggest that an aligned network (homophily score of +0.07) may be a 'strong' network, supporting the literature on collaborative approaches that argues that alignment may be an indicator of network success [10,13].
The Kitui WASH Forum homophily analysis also demonstrated the value of looking at different relationships, and specifically looking at relationships that focus more on joint working rather than surface-level interactions like information sharing. When looking at the network in 2020 (Fig 6), information sharing was strong across both sub-groups, but support was weaker in the CBM group. The homophily scores also quantify some of this misalignment, where the information-sharing network in 2020 has a stronger tendency for actors to connect with those with unlike priorities (r = -0.08) compared to the support network (r = -0.01).

PLOS WATER
Notably, even though a key County Government official who prioritized CBM (circled in black) was sharing information frequently with many other actors who also prioritized CBM, these relationships did not translate into support relationships as the same County Government official remains isolated from the CBM sub-group when looking at support relationships. On the other hand, the PM sub-group contained strong information-sharing and support ties to two County Government officials. Knowing that the PM sub-group made the most progress on their goals, this may signal that support relationships are more important to investigate in alignment analyses compared to information-sharing relationships.
Thus, these results indicate that homophily analyses of collaborative approaches should (a) investigate relationships that focus more on joint working and (b) visualize networks to understand sub-group ties. 4.2.2. Debre Birhan Learning Alliance. The Debre Birhan Learning Alliance was newly formed in May 2018 and, by 2020, was able to generate buy-in for, secure funding for, and construct a temporary Fecal Sludge Dumping site and access road in their town, as well as draft plans for a permanent site. In addition, they increased the municipal budget allocations for sanitation in their town. Their story shows important changes that occur over the development of a strong collaborative network who is able to implement impactful actions collectively. The homophily analysis revealed that before formation, the network was misaligned, with a tendency for actors to share information (r = -0.16) and work with (r = -0.08) actors who had different priorities than them ( Table 2). A year after the Learning Alliance formation in 2018, the number of ties had increased by more than 50% (see network statistics in S1 Text) but these new ties did not tend to be formed between actors with the same priority. By 2019, one year after Learning Alliance formation, actors had an even stronger tendency to connect with actors with dissimilar priorities (r = -0.22 for information-sharing and r = -0.13 for support). However, by 2020, alignment had increased significantly. Actors still tended to connect to actors with dissimilar priorities overall, but alignment did increase ( Table 2).
Visualizations strongly help tell this story by highlighting sub-groups of actors. For this analysis, because the information-sharing and support networks looked very similar, we will focus visualizations on the support relationships. From 2018 to 2020, the network gradually prioritized the FSD site, and those prioritizing the FSD grew more and more connected over time (Fig 7).
As this single prioritized activity gained traction over time, alignment first decreased as new ties were formed but appeared to not be strategically formed between those with similar priorities. In 2019, despite four actors prioritizing the FSD, only two supported one another (noted as blue circles). By 2020, alignment increased significantly, with five actors prioritizing the FSD and all supporting others who also prioritized the FSD.
Despite a negative homophily score, by 2020, the group was still able to construct the temporary FSD site, secure a location for a permanent site, and increase the municipal budget allocations for sanitation. This is despite the plethora of other priorities that existed in the network, including increasing coordination or securing commitment by the town administration. Like the Kitui WASH Forum, who participated in the sub-group mattered, as influential actors were present in the sub-group that prioritized the FSD. Yet, another factor was also at play in the Debre Birhan Learning Alliance: The other priorities by other members do not conflict with the act of constructing a temporary Fecal Sludge Dumping site. These results show the reality of trying to align priorities within a collaborative group where diverse perspectives are present. This result suggests that ambitious goals of complete alignment in collaborative groups may be too high of a bar for the reality of these approaches on the ground. Indeed, negative homophily scores and 'misalignment' may not prevent progress.

Discussion
With collaborative approaches increasingly applied in the WASH sector, and with alignment cited as a key outcome metric, it is important to understand alignment within collaborative approaches in WASH. Further, with increasing use of network analysis as a tool in the WASH sector [23][24][25], using network analysis to understand alignment is a natural fit for the WASH sector. This study starts to fill this gap. Despite the two well-functioning collaborative networks having an agreed common vision of safe and reliable sanitation or water services for the area, the networks were largely misaligned with an overall tendency of stakeholders to be connected to others with different priorities (i.e., with negative homophily scores). When looking across the five unique snapshots of the networks at different points in time, four snapshots had negative homophily scores, meaning that stakeholders had an overall tendency to connect to others with different priorities. This means that these successful networks, as a whole, were misaligned. Yet, existing literature would have suggested that a 'strong' collaborative network would be aligned, having a positive homophily score between 0 and +0.5.
We saw great variation in homophily scores across networks that were able to collaboratively implement actions, for example, how the Kitui WASH Forum support network in 2018 had a homophily score of +0.07 and was able to collectively develop and pass a County-wide Water Bill to standardize water scheme management models and support professionalized maintenance. However, the Debre Birhan Learning Alliance, despite their ability to construct a temporary Fecal Sludge Dumping site in 2020, had a negative homophily score of -0.05. Analyzing alignment over time may provide additional insights and a starting point for future work, for example the Debre Birhan Learning Alliance showing an overall positive trend of +0.08 in its homophily score from 2019 to 2020.
These results call into question the assumption that alignment is an indicator of a successful network, supporting previous work from Ogada et al. [10] which found that actors in collaborative networks tended to collaborate with different types of institutions. This would be expected in collaborative approaches that bring together diverse actors with very different priorities [21,44]. Conflict and disagreement, which may cause the misalignment, may help spur innovation and help solve complex, systemic problems. Investigating network strength through a process-focused lens, in an otherwise structure-focused body of literature on network strength [32,33], allowed for a more nuanced understanding of network strength.
Ultimately, it is the integration of this method with in-depth case knowledge that allowed for a more complete understanding of alignment. Despite misalignment in the network as a whole, sub-groups of actors with the same priorities were working together closely (not just sharing information). The sub-groups still had many intra-group connections (i.e. ties connecting actors with different priorities) which also helps to stymie "group think", where the introduction of new ideas is limited, and creates space for new ideas to flow into the subgroup [9,51,52]. Critical to understanding alignment in a collaborative group is understanding what the priorities are, where sub-groups form, and who is in those sub-groups.
A few key recommendations for future users of this method have emerged-whether used in practice to aid facilitation of collaborative approaches, or for research. First, homophily analyses should be supplemented by clear visualizations for interpretation (for example through NodeXL software [45]), if taken as standalone calculations they do not allow for full interpretation of network structures. Homophily analyses should also look at relationships that indicate working together (such as via support, training, coordination, sharing resources, or joint implementation) rather than just the sharing of information. Network analysts and implementers of collaborative approaches should both place greater emphasis on subgroups within networks, as they are an important structural aspect of how work gets done and may also help capture influence points within a network. Second, homophily analyses can help map how alignment evolves over the course of the establishment of a collaborative network, with early years creating some misalignment as new ties are formed often for reasons other than priorities, then greater alignment as the group starts to move toward action. Thus we recommend that studies of collaborative networks should look at changes over time, rather than at single snap-shots in time. Iteration at an annual frequency provided a nuanced view into network evolution, especially in a newly-formed network (Debre Birhan). We also advise researchers assessing homophily to directly interview actors about their prioritized activities rather than use other attributes as proxies, as is the current norm in network research.
We found a key limitation of using the homophily analysis to be that the calculation alone cannot tell the entire story of alignment within a network and should be supplemented by visualizations to adequately investigate sub-group alignment. A valuable addition to this method would be if a network analysis software package such as igraph could develop a metric that could reflect connectivity within a sub-group based on an attribute, accounting for random tie formation.

Conclusions and contributions
Implementers of collaborative approaches expect to build and strengthen networks of local stakeholders that can work together to improve water and sanitation services. These approaches can be designed to overcome fragmentation by fostering consensus and connecting stakeholders that share priorities. The latter goal, connecting stakeholders that share priorities, is referred to as "alignment". Yet, to date there is no evidence for if, how, or why this alignment occurs. Developing a method to quantify alignment is a critical first step.
By simultaneously mapping stakeholder priorities and relationships, we can measure and visualize alignment. Our novel approach contributes to practice by allowing organizations to use network analysis tools more effectively as an adaptive management tool to assess and monitor progress of collaborative approaches. We argue that mapping alignment and misalignment over time can help facilitators of collaborative approaches better manage their group to create sub-groups that both (a) ensure those with similar priorities are working together closely, and (b) allow some connections to others to allow them to solve complex problems and minimize group think. A comprehensive understanding of alignment can also add evidence to deepen conversations around alignment of incentives and financial flows. As these findings also lay the groundwork for quantifying and visualizing alignment, we believe that with further study and use, the metric can become a way to understand network strength by looking at alignment of subgroups.
This work also contributes both to network theory and the various theories on collaborative approaches. We build on network theory by bringing qualitatively-analyzed interview data into a homophily analysis to directly assess alignment rather than using proxies. Existing literature has largely sought to understand alignment using proxies because current network analysis tools cannot directly map alignment. We thus build on theory by expanding the range of applications of the homophily analysis [33], developing a way to understand the process through which collaborative networks align and move beyond conventional, structure-focused methods [32,35].
This study was also the first to map how alignment changes over time, documenting how actors in a collaborative network first forged new connections to many actors regardless of their priorities, followed by a gradual prioritization of an activity and the coalescing of ties as actors work together to implement the activity. Collaborative governance and other theories of collaboration have cited alignment as a key outcome of collaborative approaches, but prior to this study, there has been no effective way to map or quantify alignment.
As a result, there also has been too little investigation into how aligned collaborative groups actually are, and the extent of alignment required. We showed that while consensus on visions may be required, as suggested by previous research [2], some alignment on priorities for how that vision will be accomplished may be required within sub-groups. In our cases, collaborative networks that were able to successfully implement activities together had one or more wellconnected sub-groups of aligned actors amidst a larger network of diverse priorities for activities, but the overall network was misaligned. This reinforces the established idea a certain degree of 'misalignment' is pivotal to collaborative approaches as it allows for diverse perspectives to be brought into solutions and creates the conditions for innovation, rather than the conditions for 'group think' [10]. This shifts the conversation away from whole-network alignment and elevates the importance of the sub-group. As such, we encourage network-and systems-theorists to further investigate the role of the sub-group in applications beyond collaborative approaches, such as network strengthening and systems strengthening.
The novel method developed for this work allows researchers and practitioners to quantify and visualize alignment using network analysis and case knowledge. With these tools and evidence, future work can map how collaborative approaches align activities and trigger collective action.