Topological Analysis of Community Currency Networks: Sarafu Token Case Study

Table of Contents

1 Introduction

Digital payment systems generate transaction data that enables unprecedented detailed analysis of economic processes. This study examines the Sarafu token network, a community inclusion currency in Kenya deployed during the COVID-19 emergency as part of humanitarian aid. The research applies network science methods to analyze transaction patterns, with particular focus on topological categorization of cyclic and acyclic components and their role in currency circulation.

The Sarafu network represents a digital community currency system organized by Grassroots Economics, a non-profit organization. During the analyzed period, the system functioned as an emergency cash transfer program co-designed with the Kenyan Red Cross. Community Inclusion Currencies are local voucher systems designed for humanitarian cash transfers, restricted to predefined geographic regions or participant networks to stimulate local economic development.

2 Methodology

2.1 Network Construction

The payment system is modeled as a directed, weighted, temporal network where nodes represent system participants and timestamped directed weighted links correspond to transactions. For topological analysis, transactions are temporally aggregated into weighted directed links, while temporal aspects are preserved for circulation analysis.

2.2 Component Analysis

The methodology involves identifying strongly connected components (SCCs) and their hierarchical structure. Components are categorized as cyclic (containing directed cycles) or acyclic (tree-like structures). This categorization helps distinguish between different user engagement patterns and currency circulation behaviors.

2.3 Null Models

Randomized null models are employed to assess the statistical significance of observed topological patterns. These models help determine whether the prevalence of certain component types exceeds what would be expected by chance in a random network with similar basic properties.

3 Technical Framework

3.1 Mathematical Formulation

The network is formally defined as $G = (V, E, W, T)$ where $V$ is the set of vertices (users), $E \subseteq V \times V$ is the set of edges (transactions), $W: E \rightarrow \mathbb{R}^+$ assigns weights to edges (transaction amounts), and $T: E \rightarrow \mathbb{R}^+$ assigns timestamps.

The currency circulation in component $C$ is measured as:

$$R(C) = \frac{\sum_{e \in E(C)} w(e)}{\max_{v \in V(C)} \sum_{e \in E^{out}(v)} w(e)}$$

where $E(C)$ denotes edges within component $C$, $w(e)$ is the weight of edge $e$, and $E^{out}(v)$ represents outgoing edges from vertex $v$.

3.2 Algorithm Implementation

The following pseudocode demonstrates the component analysis algorithm:

function analyze_currency_network(G):
    # Identify strongly connected components
    SCCs = tarjan_strongly_connected_components(G)
    
    # Build condensation graph
    DAG = condense_graph(G, SCCs)
    
    # Classify components
    cyclic_components = []
    acyclic_components = []
    
    for component in SCCs:
        if is_cyclic(component):
            cyclic_components.append(component)
        else:
            acyclic_components.append(component)
    
    # Calculate circulation metrics
    metrics = {}
    for component in cyclic_components + acyclic_components:
        metrics[component] = calculate_circulation(component)
    
    return cyclic_components, acyclic_components, metrics

4 Experimental Results

4.1 Component Distribution

The analysis revealed a significant presence of strongly connected components compared to randomized null models, demonstrating the importance of cycles in economic networks. Cyclic components showed higher currency recirculation rates, indicating active trading communities where the currency circulated multiple times among participants.

In acyclic components, the most significant triad pattern suggested the presence of users collecting currency from accounts active only once, potentially indicating system misuse. Small isolated groups of users active only once were also identified, suggesting users merely testing the system without sustained engagement.

4.2 Temporal Analysis

Temporal analysis of transaction patterns revealed distinct circulation dynamics. Cyclic components maintained consistent activity over time, while acyclic components showed sporadic engagement patterns. The visualization of component evolution over time demonstrated how user engagement strategies evolved throughout the emergency period.

5 Original Analysis

This research represents a significant advancement in applying network science to community currency systems, building upon foundational work in economic network analysis. The topological approach developed by Criscione provides a rigorous framework for understanding currency circulation patterns that extends beyond traditional economic metrics. Compared to conventional financial network analysis approaches used in studies of banking systems (Battiston et al., 2016) or cryptocurrency networks (Kondor et al., 2014), this methodology offers unique insights into community-based economic systems.

The identification of cyclic components as indicators of healthy currency circulation aligns with economic theory emphasizing the velocity of money as a key economic indicator. However, the network perspective adds spatial and relational dimensions to this understanding. The significant presence of cyclic components compared to null models suggests that successful community currencies naturally develop circular flow patterns, similar to the metabolic networks studied in systems biology (Jeong et al., 2000).

The detection of potentially problematic usage patterns through acyclic component analysis demonstrates the practical utility of this approach for currency system management. This capability is particularly valuable for humanitarian applications where resource optimization is critical. The methods developed here could be integrated with machine learning approaches for anomaly detection, similar to techniques used in financial fraud detection (Phua et al., 2010), but adapted for the unique characteristics of community currency systems.

From a technical perspective, the combination of topological analysis with temporal dynamics addresses a key limitation in many network studies that treat systems as static. The approach shares methodological similarities with temporal network analysis in social systems (Holme & Saramäki, 2012), but applies these techniques to economic behavior in crisis contexts. Future work could benefit from incorporating multilayer network frameworks to capture the interplay between different types of economic relationships.

6 Applications and Future Directions

The methodology developed in this research has broad applications beyond the specific case study:

• Humanitarian Aid Optimization: Real-time monitoring of currency circulation in emergency response programs
• Local Economic Development: Designing community currencies that maximize local economic impact
• Financial Inclusion: Understanding adoption patterns in underserved communities
• Policy Assessment: Quantitative evaluation of monetary interventions and their network effects

Future research directions include:

• Integration with agent-based modeling to simulate intervention impacts
• Development of real-time monitoring dashboards for currency administrators
• Cross-cultural comparative studies of community currency networks
• Machine learning applications for predictive analysis of currency success factors

7 References

1. Battiston, S., et al. (2016). Complexity theory and financial regulation. Science, 351(6275), 818-819.
2. Holme, P., & Saramäki, J. (2012). Temporal networks. Physics reports, 519(3), 97-125.
3. Jeong, H., et al. (2000). The large-scale organization of metabolic networks. Nature, 407(6804), 651-654.
4. Kondor, D., et al. (2014). Do the rich get richer? An empirical analysis of the Bitcoin transaction network. PloS one, 9(2), e86197.
5. Phua, C., et al. (2010). A comprehensive survey of data mining-based fraud detection research. arXiv preprint arXiv:1009.6119.
6. Grassroots Economics. (2023). Community Inclusion Currencies: Design Principles. Retrieved from grassrootsconomics.org