# Analyzing the Bitcoin Network: The First Four Years
## 6 Analysis and Results
### Network Analysis
#### 6.2.3 Clustering in the Bitcoin Network  
In this section, the network measure average clustering coefficient is going to be applied on the time, business, and country level to investigate the global cliquishness in the graph. Furthermore, it serves as a first indicator of the small world phenomenon within the Bitcoin network. Analyzing the existence of small world networks requires high computation power and is therefore conducted on minor subgraphs on the country and business level. When considering the average clustering measure over time in Figure 33, one can see rather high coefficients in comparison to random networks, indicating a small world network. The measure was computed on a monthly basis for the years 2012 and 2013. For the year 2011 the calculation was done quarterly. The years 2009 and 2010 were omitted from the analysis due to very low activity in the network and lots of transactions between same entities. The average clustering coefficient decreases with increasing activity in the network. In quarter two and three of 2011 the lowest coefficients were computed, while the user activity surged in that time period. The same effect can be noted for August 2012 and March 2013. Hence, more user activity in the network reduces the global cliquishness in the Bitcoin economy. The average clustering coefficients for different business categories are depicted in Figure 34. Because of limited computation power, the coefficients for the gambling and exchange business were calculated on subgraphs (January-April 2013). The gambling business has the highest average clustering coefficient with around 0.5. This indicates that the gambling business is tightly connected and has a high density of nodes. In contrast, the computed coefficients for other businesses are rather low but indicate the existence of the small world phenomenon. The mining business has a low average clustering coefficient with 0.012, indicating a rather separated engagement of the miners in the network. Figure 32: Betweenness and Closeness Centrality for the Wallets Business. Figure 35 shows the average clustering coefficient for selected countries. The coefficients for the major markets U.S. and Germany were calculated on subgraphs (January-April 2013). China and the U.S. have the highest avg. clustering coefficient with 0.116 and 0.130, respectively. These are also Bitcoin markets that are mainly driven by the gambling business, which has a very high average clustering coefficient. The coefficients for the other Bitcoin markets are in the range from around 0.05 to 0.08, indicating the existence of the small world phenomenon when considering the average clustering coefficient for random networks. In the following, the hypothesis of the small world character will be tested on two business categories and four countries as representatives for these aggregation levels. To determine the existence of a small world graph one has to calculate the average clustering coefficient and the average shortest path length of the graph in question. In addition, a random graph with the same number of nodes and edges needs to be generated. When comparing the computed network measures the average clustering coefficient of the Bitcoin network has to be significantly higher than the one of the random network (\(\overline{C}_{Bitcoin}\gg\overline{C}_{Random}\)) while the average shortest path length has to be rather low and is approximately the same (\(ASPL_{Bitcoin}\ \cong\ ASPL_{Random}\)). The calculation of the average shortest path length requires high computation power for large-scale graphs and subgraphs as it is the case with the Bitcoin network. Hence, testing for the small world phenomenon is done on minor subgraphs on the country and business level. Figure 34: Average Clustering Coefficient for Business Categories. Figure 33: Average Clustering Coefficient over Time. Table 5 shows the results of the small world analysis. On the country level the existence of the small world phenomenon could be approved for all considered countries.