This post contains an MA essay that touches on transdisciplinarity, through arguing Indian Ocean trade networks can be seen as complex.

Introduction

It is becoming increasingly common to think of the Middle Ages as global. The fact that Past and Present dedicated an entire issue to the topic in 2018 (Holmes & Standen, 2018) shows how popular an approach it is becoming. Two concepts and structures often invoked when analysing the Global Middle Ages are the idea of a ‘world system’ and also networks (Abu-Lughod, 1991) (Shepard, 2018). This paper shall analyse the extent to which these two concepts can engage in meaningful dialogue with each other. In particular, it will look at if complex network theory can alter our understanding of the medieval world system. It will do this by looking at if a network of the Indian Ocean world compiled by the author can be described as complex. A network is a series of nodes connected by edges, the features that make a network complex will be explained in the results section. This is not the first paper to apply complex network theory to the Middle Ages, Sindbaek (2007) has applied it successfully to the Viking world. However, this shall be the first attempt to apply it to the early medieval Indian Ocean world. The central thrust behind this paper is that if we can talk of the early medieval Viking and Indian Ocean worlds as both complex, then can we talk about the world system in its entirety as a complex system? The idea of a ‘world system’ was first introduced to the Middle Ages by Abu-Lughod (1991). It describes how the world is connected through different interacting circuits and parts forming a system of exchange. For Abu-Lughod, this system emerged in the thirteenth century, but as will become clear it was present much earlier. Some authors have hinted at the possibility of the medieval world system being viewed as a complex, Dudbridge (2018, pp. 314-315) raises the possibility of using systems biology to understand the world system. However, no systematic attempt has been made to fully analyse the possibility of making a connection between complex network theory and the medieval world system. This paper shall attempt to do this.

It will do this in three sections. The first section will outline the methodology employed for this essay, it will look at how the network analysis was carried out and will examine its limitations. The second section will include the results of the analysis and will examine if the compiled network can be described as a complex network. The final section shall discuss the implications of the results for understanding the world system. The essay shall conclude with a radical call for transdisciplinarity to increase our understanding of the world system.

Methodology

It is now necessary to outline how the network analysis was conducted. The data was collected from five articles. These were chosen through a search of Web of Science using the terms ‘medieval Indian Ocean trade’ and ‘medieval Indian Ocean world.’ Some articles were filtered out and not chosen for data entry. This was usually because they did not fit the temporal limits of the essay, 500-1000, or because they were irrelevant to the topic. It should highlighted that this study is only an preliminary endeavour and so should not be considered comprehensive. Further research will need to be conducted to verify the findings of this essay. The data was entered into Microsoft Excel (Microsoft, 2021). It was put into a nodes table, with each node representing a location from the article, and a source-target table which had the connections between the different places. Appendix A lists the locations in the network and the articles they were taken from. A connection was established if a location shared archaeological material with another. If an article cited literary evidence this was ignored. This is primarily an archaeological paper. Once the tables were complete the data was imported into Gephi (The Gephi Consortium, 2017). Gephi is a network visualisation and analysis computer programme. The statistics used in the results section of this essay derived from this programme. There were a total of 54 nodes in the network and 112 edges. Figure 1 shows the network compiled by the above methodology. Having outlined the methodology of this paper, it is now necessary to proceed and list more limitations of this essay.

Figure 1: Screenshot of Network (Data from author’s own work)

There are two types of limiting factors with regards to what this study can tell us. The first concerns the limitations of the network analysis itself. One limitation is the fact that this essay only contains data from 500-1000. This temporal framework was chosen for two reasons. Firstly, to make sure sites which are from different parts of medieval era are not erroneously seen as connected when in fact they are from a different time. Secondly, to allow a more direct comparison with Sindbaek’s (2007) study of how complex networks apply to the early medieval Northern Europe. A second factor to consider is that some of the nodes are more vague than others. Some articles offered specific locations such as ‘Unguja Ukuu’, while others were more broad and named modern countries such as ‘China’ and ‘India’. The latter were still included in the essay, as to avoid missing too many connections. A further factor to consider is that a connection between two places does not mean they had constant or instantaneous contact. Travel between different parts of the Indian Ocean, even in the later twelfth and thirteenth centuries, could take up to six months (Abu Lughod, 1991, p. 16). Finally, the network created for this essay is static, the data was not precise enough to create a dynamic graph. This makes it harder to analyse change over time. With the limitations of the network analysis considered, it is now worth considering some of the limitations of the material evidence.

The first factor to consider, with regards to the evidence, is that the material presented here only represents the movement of physical material objects. It does not consider how ideas spread across the Indian Ocean or how ideas are connected to objects. Secondly, we must also accept the fact that the presence of evidence in two sites does not necessarily mean that two places are connected. It does, however, indicate an increased likelihood of them being connected or at least that they were part of the same system of exchange. Finally, the evidence used in this essay derives from a variety of material forms, including, but not limited to, ceramics, glass and ship materials. There is not space here to go into depth about each evidence type here, but it is hoped the last two paragraphs have raised some of the associated methodological and evidence-based issues that limited this study. This finishes the methodology section of the essay.

Results

Having outlined the methodology of the essay and the pertinent limitations, the paper will now proceed to present the results of the network analysis. It will do this in four subsections which will cover different features of complex networks. Each subsection will examine if the compiled network of the Indian Ocean has these features. This will help to reveal if the early medieval Indian Ocean can be seen as complex and subsequently, in the discussion section, help us to analyse whether the world system can be described as complex.

The first feature complex networks are generally considered to have is a ‘small world’ effect. A ‘small world’ effect refers to the fact that there is generally a small path between any two nodes (Albert & Barabasi, 2002, p. 2) (Newman, 2003, p. 181) (Strogatz, 2001, p. 278). The most famous example derives from the concept of ‘six degrees of separation’. This idea suggests that there is on average people are separated from each other by six people. Meanwhile, Barabasi (2002, pp. 34-39) has suggested there are on average nineteenth degrees of separation between web pages. There are several statistics which help us to identify if the Indian Ocean world can be seen as a ‘small world’ like the World Wide Web or social contacts. The first is the average path length. This was 2.7330538085255065. This is far lower than 6 or 19 and so it is fair to say that the network in this study can be described as having a ‘small world’ effect. Further evidence confirms this. The closeness centrality of each node, which calculates the distance from a giving starting node to all other nodes in the network, is shown in figure 2. The x-axis displays the distance to all other nodes in the network for each node, whereas the y-axis shows the number of nodes with a particular distance. The closeness centrality for each node is between 0 and 1 indicating that there is on average less than one connection between one node to all other nodes in the network. This shows that the data has a ‘small world’ effect. To summarise, it is clear from this that the Indian Ocean was a ‘small world’ and that it has at least one feature of a complex network. However, it remains to be seen if it has the other features complex networks have.

Figure 2: Closeness Centrality Distribution (Data from author’s own work)

The second feature that complex networks tend to have is clustering. This is the tendency for nodes to form into split groups or as Newman (2003, p 183.) puts it the friend of your friend is likely to be your friend. The first statistic worth analysing is the average clustering coefficient. This metric is on a scale of 0 to 1, with a higher score indicating that individuals tend to be found in groups. The average clustering coefficient for the network was 0.425. This seems to indicate that clustering is not that apparent in the network and raises questions about the Indian Ocean world having this characteristic of a complex network. However, two pieces of evidence suggest that the average clustering coefficient does not tell the whole story. The first is the number of triangles in the network which was 52. This statistic indicates the extent nodes form into groups of 3, in which each node is connected to every other node. The score presented here suggests there are a high amount of communities in the network and is therefore evidence of clustering. A modularity algorithm (Blondel, Guillaume, Lambiotte & Lefebvre, 2008) was also ran on the network. This detected a different number of communities to the triangle measurement. Overall, it identified a total of six communities. Figure 3 displays each community in a different colour. While 6 communities does not seem much, we must remember that there are 54 nodes in the network and so there is around 9 people per group. Small group sizes, such as these, indicate the presence of clustering in the network, even if the average clustering coefficient seems at odd with this. Furthermore, it is possible that the average clustering coefficient is only so low because of the high degree of connectivity in the network, which itself is a sign of a complex network. Regardless, it can be said tentatively that there is evidence of clustering in the network and that it has this feature of complexity.

Figure 3: Modularity Class of Nodes (Data from author’s own work)

The third feature that complex networks have is that the degree distribution (how many edges a node has) tends to follow a power-law (Barabasi & Albert 1999). Networks with such a feature are called scale-free (Strogatz, 2001, p. 214). In such networks, there tend to be some nodes which are more highly connected than others. Figure 4 shows the degree distribution of the Indian Ocean network. The x-axis represents the degree of nodes, whereas the y-axis indicates the count of nodes with a particular degree. As the data shows, there are 16 nodes with a degree of 1, whereas there are only 3 nodes with a degree of 7 and 1 node with a degree of 22. Overall, there does seem to be some nodes which are more highly connected than others. The graph also shows a decay, which is central to it being scale free, there seem to be a few nodes with a high degree and many with a low degree. Nevertheless, a comparison of figure 4 and figure 5 complicates the issue. Figure 5 portrays four real world networks. In figure 5 we see the decay for each graph is more steady than in figure 4. In figure 4, we also see a sudden drop from 15 nodes having a degree of 2 to 2 nodes having a degree of 3. This decline is much more rapid than in other networks which are termed complex (see figure 5). Furthermore, the count of nodes also increases again for having a degree of 4 and 5. There were five nodes with a degree of 4 and 5. This increase goes against the continuous decline we see in the real world networks of figure 5. This would seem to indicate that the degree distribution of the network is only partly scale-free and that there are some anomalous results in the network. Nevertheless, there does seem to be a general decline in figure 4, even if it is not straight forward. It should also be noted that the scale-free property is common but not universal to complex networks (Strogatz, 2001, p. 219). With this and the general decay in the results took into consideration, it appears that would be wrong to dismiss the possibility of the network being complex based on the data.

Figure 4: Degree Distribution of Network (Data from author’s own work)

Figure 5: Degree Distributions of Real World Networks (Strogatz, 2001, p. 273)

The final feature complex networks tend to have relates to their robustness against attacks. Many complex systems display a degree of tolerance against errors, if the attacks are random. Meanwhile, if the attack is targeted at the hubs (the most connected nodes) the network tends to be vulnerable (Albert & Barabasi, 2002, p. 44). To analyse whether the Indian Ocean network has these features, this paper will use the technique of removing nodes randomly and then compare this to taking them away based on their centrality measures (Iyer, Killingback, Sundaram & Wang, 2013). Figure 6 shows what happened when five nodes were removed randomly. A glance at the figure reveals that for the most part the graph remained highly connected. There was only one community that was completely isolated from the rest of the network (see bottom of figure). This indicates, for the most part, that the network displays resilience against random attacks, The next step in examining the network’s robustness was to remove five of the most prominent nodes. The five nodes with the highest closeness centrality were chosen to be removed. This simulates the removal of the hubs of the network. Figure 7 shows the network with the key nodes removed. In comparison to the results from figure 6, it is clear that many more nodes are isolated and cut off from the main network. This indicates that the network has the robustness characteristic of complex networks- a strong defence against random attacks, but a weakness against attacks on the hubs. Therefore, the network has another feature that complex networks have.

Figure 6: Graph with Random Node Removal (Data from author’s own work)

Figure 7: Graph with Selective Node Removal (Data from author’s own work) Discussion

The network compiled for this essay displays the four main features of complex networks suggesting that the Indian Ocean can be seen as a complex network. This section will examine how these four features of a complex network alter our understanding of the world system. However, it is first necessary to establish a connection between the Indian Ocean network and the world system. The way to do this is to remphasise Sindbaek (2007) has already proven the Northern Europe can be seen as a complex network. This, alongside with the Indian Ocean being seen as a complex network, suggests a good part of the early medieval world can be seen as complex. Critics could raise that there might have existed two isolated complex networks rather than a single unified world system. However, when we take into consideration that world systems theory allows for different circuits or spheres that overlap with each other the possibility of a single world system with complex features seems more plausbile. Abu-Lughod (1991, p. 33) with reference to a later timeframe, divides the world system into three main parts: Western Europe, the Middle East and the Far East We can do the same for the early medieval world and suggest Northern Europe and the Indian Ocean formed different circuits of the same world system. To phrase it differently, there existed a network of networks. This does not mean the Indian Ocean and Northern Europe were directly connected, but it does suggest that what happened in one of these spheres might have had direct cosequences in another. As Abu-Lughod (1991, p. 32), puts it ‘no world system is global, in the sense that all parts articulate evenly with one another.’ Nevertheless, there were also a number of nodes in the netwok, such as Fusat and Antioch, which suggest the connections the Indian Ocean had went beyond its own sphere, even if the majority of connections took place within its own limits. Further research could confirm these findings, the study of different parts of the Africa and Eurasia and their connections, could make the presence of a world system more clear. This would especially be true if there was an emphasis on transconintental connections. Regardless, it now seems plausbile to put forward a pleminary thesis that there was an early medieval world system and that it was complex.

With a connection between the complex networks and the world system established, it remains to see how the features of a complex network might alter our understanding of the world system. The first feature to discuss is the ‘small world’ effect. Different spheres of the world system likely had, as Sindbaek (2007, p. 61) and this paper have proven, a ‘small world’ effect. The Indian Ocean and Northern Europe were both small worlds. This would seem to indicate that different spheres of the world system had high levels of connectivity within them, even if there were not many connections between different spheres. This emphasises the importance of viewing the world system as composed of different parts as Abu-Lughod (1991, p. 33) and Beaujard and Fee (2005, p. 43) have suggested.

The presence of clustering in the Indian Ocean and Viking world networks further emphasise the need to view the world system as composed of many small groups forming a wider system. Much of the network, even within spheres, was clustered. Therefore, like above, we need to stop thinking of the world system as distant parts connecting instantaneously, but to view it as an intricate web of smaller pieces joining together to form a wider system. This again highlights the need to view the world system as smaller pieces joining together.

The last two features that needs to be discussed is degree distribution and robustness. The Indian Ocean network had a few nodes with really high connections and many with few connections. This suggests we need to view the world system as composed of hubs facilitating connections between different parts of the world. The implications of this are clear, if the hubs were attacked, then the connections between different parts of the world system would mostly fail. The early medieval world system was therefore vulnerable if a certain city or location that was key was attacked or cut off by other means. Nevertheless, random attacks would not have harmed it much. Regardless, the levels of robustness the world system had is now clear.

To summarise, the Indian Ocean network and Sindbaek’s (2007) Viking network clarify our understanding of the world system in several ways. Firstly, they remphasise the need to view it as composed of many small interwoven pieces. Secondly, they highlight the general robustness of the world system, even if it was vulnerable to attacks on its hubs. These are the two main ways in which complex network theory alters our understanding of the world system.

Conclusion

This paper has proven that the Indian Ocean from 500-1000 was a complex network and consequentially shown that the world system from this period also displayed features of complexity. It did this in three sections. The first introduced the methodology of the essay, in particular it discussed how the network analysis was carried out and highligted some of the limitations of the essay. The second section looked at the results of the network analysis, it concluded that the Indian Ocean network mostly had features of a complex network. The final section took forward these findings and suggested how they might alter our understanding of the world system.

However, this project is just the beginning. Further research is needed. More parts of the world need analysing and transphere analysis needs to be conducted. Furthermore, there are many complex networks in the world, not just systems of exchange. Cells are complex networks of chemicals, the Internet is a complex network of computers and routers. Likewise, the movie industry is a complex network of actors, while language is a network of words (Albert & Barabasi, 2002, pp. 49-54). A radical transdisciplinary approach is therefore required to increase our understanding of the world system, as it shares many of the same features as networks from other disciplines. This paper therefore ends with a call to arms to break disciplinary boundaries, so we might increase our understanding of the world system. As we now know the early medieval world system was complex, we need to see how other disciplines might inform our discussion of it. Regardless, this paper has proven that the early medieval Indian Ocean was a complex system and, along with the work of Sindbaek (2007), has shown that the medieval world system itself was a complex network, even if further research is needed to verify the findings of this preliminary study.

Appendix A: List of Sites and Articles They Were Taken From

Tumbe	(LaViolette and Fleisher, 2013)
Manda	(LaViolette and Fleisher, 2013)
Unguja Ukuu	(LaViolette and Fleisher, 2013) (Flecker, 2001) (Pollard and Kinyera, 2017)
Kilwa	(LaViolette and Fleisher, 2013) (Pollard and Kinyera,2017)
Shanga	(LaViolette and Fleisher, 2013)
Sasanian- Islamic	(LaViolette and Fleisher, 2013) (Pollard and Kinyera, 2017)
Siraf	(LaViolette and Fleisher, 2013) (Flecker, 2001) (Pollard and Kinyera, 2017)
China	(LaViolette and Fleisher, 2013) (Flecker, 2001)
Comoros	(LaViolette and Fleisher, 2013) (Flecker, 2001)
Belitung	(Flecker, 2001)
Changsha	(Flecker, 2001)
Yue	(Flecker, 2001)
India	(Flecker, 2001)
Yangzhou	(Flecker, 2001)
Southeast Asia	(Flecker, 2001)
Sri Lanka	(Flecker, 2001)
Indus Valley	(Flecker, 2001)
Persian Gulf	(Flecker, 2001)
Red Sea	(Flecker, 2001)
Samarra	(Flecker, 2001)
Nishur	(Flecker, 2001)
Fusat	(Flecker, 2001) (Pollard and Kinyera, 2017)
Antioch	(Flecker, 2001)
Sohar	(Flecker, 2001)
Palembang	(Flecker, 2001)
Prambanan Temple	(Flecker, 2001)
Laem Pho	(Flecker, 2001)
Ko Kho Khao	(Flecker, 2001)
Bagamoyo	(Pollard and Kinyera, 2017)
Aydhab	(Pollard and Kinyera, 2017)
Chibuene	(Pollard and Kinyera, 2017) (Pollard, Duarte and Duarte, 2018)
Lamu	(Pollard and Kinyera, 2017)
Madagascar	(Pollard and Kinyera, 2017)
Kharg Island	(Pollard and Kinyera, 2017)
Fukuchani	(Pollard and Kinyera, 2017)
Ras Hufan	(Pollard and Kinyera, 2017)
Egypt	(Pollard and Kinyera, 2017)
Susa	(Pollard and Kinyera, 2017)
Tell Abu Sarifa	(Pollard and Kinyera, 2017)
Zimbabwe	(Pollard and Kinyera, 2017)
Botswana	(Pollard and Kinyera, 2017)
South Africa	(Pollard and Kinyera, 2017)
Maganbani	(Pollard and Kinyera, 2017)
Kaole Village	(Pollard and Kinyera, 2017)
Mso Bay	(Pollard and Kinyera, 2017)
Mikumbi	(Pollard and Kinyera, 2017)
Jiwe la Jahazi	(Pollard and Kinyera, 2017)
Namakuli	(Pollard, Duarte and Duarte, 2018)
Nhanluqui	(Pollard, Duarte and Duarte, 2018)
Manda	(Zhao, 2015)
Fanchang	(Zhao, 2015)
Dembeni	(Zhao, 2015)
Mogadishu	(Zhao, 2015)
Mteza	(Zhao, 2015)

Bibliography

Abu-Lughod, J (1991). Before European Hegemony: The World System A.D 1250-1350.
Oxford: Oxford University Press.

Albert, R and Barabasi, A (1999). Emergence of Scaling in Random Networks. Science, 286
(5439), 509-512. [Online]. Available at https://science.sciencemag.org/content/286/5439/509 [Accessed 27 April 2021}

Albert, R and Barabasi, A. (2002). Statistical Mechanics of Complex Networks. Reviews of Modern Physics, 74 (1), 47-97. [Online]. Available at https://arxiv.org/pdf/condmat/0106096.pdf [Accessed 27 April 2021].

Barabasi, A (2002). Linked: The New Scinece of Networks. New York: Basic Books.

Beaujard, P and Fee, S. (2005). The Indian Ocean in Eurasian and African World-Systems Before the Sixteenth Century. Journal of World History, 16 (4), 411-465. [Online]. Available at https://www.jstor.org/stable/20079346?seq=1 [Accessed 27 April 2021].

Blondel, V.D, Guillaume, J.L, Lambiotte, R and Lefebvre, E. (2008). Fast Unfolding of
Communities in Large Networks. Journal of Statistical Mechanics: Theory and Experiment,
2008 (10), 1-12. [Online] Available at https://arxiv.org/pdf/0803.0476.pdf [Accessed 27 April 2021]

Duarte, R, Duarte Y.T and Pollard, E. (2018). Settlement and Trade from AD 500 to 1800 at Angoche, Mozambique. African Archaeological Review, 35 (3), 443-471. [Online]. Available at https://link.springer.com/article/10.1007/s10437-018-9308-0 [Accessed 27 April 2021].

Dudbridge, G. (2018). Reworking the World System Paradigm. Past and Present, 238, (13), 297-316. [Online]. Available at https://academic.oup.com/past/article/238/suppl_13/297/5230765?login=true [Accessed 27 April 2021].

Flecker, M. (2001). A ninth-century AD Arab or Indian Shipwreck in Indonesia: First Evidence for Direct Trade With China. World Archaeology, 32 (3), 335-354. [Online]. Available at https://www-jstororg.libproxy.york.ac.uk/stable/827926?sid=primo&seq=1#metadata_info_tab_contents
[Accessed 27 April 2021].

Fleisher, J and LaViolette A. (2013). The Early Swahili Trade Village of Tumbe, Pemba Island, Tanzania, AD 600–950. Antiquity 87 (338) 1151-1168. [Online]. Available at https://www.cambridge.org/core/journals/antiquity/article/abs/early-swahili-trade-village-oftumbe-pemba-island-tanzania-ad-600950/96E5356A34B749A056921E27371A05A0
[Accessed 27 April 2021].

Holmes, C and Standen, N. (2018). Introduction: Towards a Global Middle Ages. Past and Present, 238 (13), 1-44. [Online]. Available at https://academic.oup.com/past/article/238/suppl_13/1/5230769 [Accessed 27 April 2021].

Iyer, S, Killingback, T, Sundaram, B & Wang, Z. (2013). Attack Robustness and Centrality of Complex Networks. PLos ONE, 8 (1), 1-17. [Online]. Available at https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0059613 [Accessed 27 April 2021].

Kinyera, O.C and Pollard, E. (2017). The Swahili Coast and the Indian Ocean Trade Patterns in the 7th–10th Centuries CE. Journal of Southern African Studies, 43 (5), 927-947. [Online]. Available at https://www.tandfonline.com/doi/abs/10.1080/03057070.2017.1345266
[Accessed 27 April 2021].

Microsoft (2021). Microsoft Excel. [Computer Programme]. Available https://www.microsoft.com/en-gb/microsoft-365/excel [Accessed 27 April 2021].

Newman, M.E. J. (2003). The Structure and Function of Complex Networks. SIAM Review,
45 (2), 167-256. [Online]. Availaible at https://epubs.siam.org/doi/abs/10.1137/s003614450342480 [Accessed 27 April 2021].

Shephard, J. (2018). Networks. Past and Present, 238 (13), 116-157. [Online]. Available at https://academic.oup.com/past/article/238/suppl_13/116/5230773?login=true [Accessed 27 April 2021].

Sindbaek, S.M, (2007). The Small World of The Vikings: Networks in Early Medieval
Communication and Exchange. Norwegian Archaeological Review, 40 (1), 59-74. [Online]. Available at https://www.tandfonline.com/doi/abs/10.1080/00293650701327619 [Accessed
27 April 2021].

Strogatz, S.H (2001). Exploring Complex Networks. Nature, 410 (6825), 268-276. [Online].
Available at https://www.nature.com/articles/35065725. [Accessed 27 April 2021].

The Gephi Consortium (2017). Gephi. [Computer Programme]. Available https://gephi.org/ [Accessed 27 April 2021].

Zhao, B. ( 2015). La Céramique Chinoise Importée En Afrique Orientale (IXe-XVIe Siècles):
Un Cas De Changement De Valeur Marchande Et Symbolique Dans Le Commerce Global. Afriques : Débats, Méthodes Et Terrains D’histoire, 6 (6). [Online]. Available at https://apps.webofknowledge.com/full_record.do?product=WOS&search_mode=GeneralSear ch&qid=3&SID=F6rExvv3Eev1VGwdOwG&page=3&doc=28. [Accessed 27 April 2021].