Uncovering the Hidden Routes: Algorithms for Identifying Paths and Missing Links in Trade Networks

A network is a simple yet powerful tool for representing a set of relations in the real world. For instance, to represent direct business relations between several people, we can sketch a network where each person is represented by a node and any two people that have done business together are connected by a link. A naive analysis of this network gives a picture of the direct connections between individuals, that is, who has done business, in person, with whom. However, for several network applications it is important to observe more complicated structures, other than the direct connections between the nodes. An example comes from applications in trade networks, where goods are exchanged between several people. In this case, it is important to keep track of the paths that specific goods have traversed in a network; in other words, we want to know the exact sequence of nodes through which a specific item was exchanged. Unfortunately, in some studies of trade networks we may not always know the exact path that certain items followed in the network. This is frequently the case with networks that represent trade relations between sites in an earlier historical period; knowledge of the exact trade paths in such networks has not survived and only fragmentary data is available (Sindbæk 2007, 2013; see in this volume Peeples et al. 2016). The same problem also arises in modern trade networks, when the transactions involved are the result of illegal activities. Such an example is the modern trade network in illicit antiquities. During recent decades, thousands of antiquities were illegally excavated worldwide and exchanged via a global trade network. During the late 1990s and 2000s, the combined efforts of forensic archaeologists and police investigators uncovered a considerable part of the trade network that handled illicit Italian and Greek antiquities in particular (Gill and Chippindale 2006; Gill and Tsirogiannis 2011; Godart et al. 2008). However, a large part of the activities that took place within this network remain unknown and there are some transactions that police investigations were not able to trace.

Network Perspectives on the Past: Tackling the Challenges

As his keynote address to the 1990 Sunbelt Social Networks conference, Mark Granovetter presented a paper entitled ‘The Myth of Social Network Analysis as a Special Method in the Social Sciences’ (Granovetter 1990). In it, he described how the popular social network theory he proposed, ‘The Strength of Weak Ties’ (Granovetter 1973), was like a spectre that haunted his academic career: although he subsequently pursued other research interests, he found that ‘as I got more deeply into any subject, network ideas kept coming in the back door’. He concluded that social network analysis (SNA) is not a ‘special’ method in social science, because ‘no part of social life can be properly analysed without seeing how it is fundamentally embedded in networks of social relations’ (Granovetter 1990: 15). However, he noted that to many, SNA is an alien concept: ‘we need to remember that there are many scholars outside the house of social network analysis who think in a relational way but don’t see the kinship with network methods and ideas’ (Granovetter 1990: 15). This observation echoes the current position of network studies in archaeology and history. Few would argue that relationships between social entities are not important for understanding past social processes. However, more explicit application of network theories and methods is not yet a mainstream part of our disciplines. Although it is the case that some researchers are not aware of the advantages such perspectives might offer, the current ‘niche’ status of network applications in archaeological and historical research relates to a more general misperception: that network concepts and methodologies per se are simply not appropriate for use in research in these disciplines. This volume aims to address both issues: the contributions in this volume demonstrate both the enormous potential of network methodologies, and also—and perhaps more importantly—acknowledge and address a range of perceived problems and reservations relating to the application of network perspectives to the study of the past, thereby encouraging and enabling their wider use in archaeology and history. The full diversity of network perspectives has only been introduced in our disciplines relatively recently.

Can Archaeological Models Always Fulfil our Prejudices?

The past few years have seen a significant growth in the use of quantitative models in archaeology. Such modelling has a long, albeit uneven, history, using ideas going back to Christaller’s (1933) use of Dirichlet/Voronoi tessellations of space in the early 20th century to construct ‘central places’. These elementary techniques for geometrizing social relations survived as late as the 1980s, most simply supplemented or replaced by other low-technology, ‘ruler and compass’ methods, such as Renfrew’s XTENT model (Renfrew 1975a, 1975b; Renfrew and Level 1979). By that time, archaeological modelling (e.g. Clarke 1968, 1977; Johnson 1977) was already incorporating the graph theory techniques of the social geographers, exemplified by the burgeoning network modelling of proximal point analysis (PPA) (e.g. Terrell 1977, 1986) and by the network-based spatial interaction models (SIMs) of the social planners and transport modellers (e.g. Wilson 1970; Wilson and Bennett 1986). However, even when adapted to historical processes (Rihll and Wilson 1987, 1991), such quantitative models were not part of the archaeological mainstream and limitations on computer power and cost meant that they had only restricted application. By the 1990s, these limitations were reinforced by a post-processual critique which led to a shift in emphasis in archaeology towards viewing space as a construct of human activity, a movement from ‘space to place’ (Hirsch 1995). Although SIMs had led this shift by downplaying the role of geography in characterizing social interactions, the dialogue about quantitative modelling turned against its reductive nature, even to the extent of shying away from mathematical analysis (e.g. Sheppard 2001). However, cheap computer power and the ready availability of commercial software packages have led to a revival in network methods. See Lock and Pouncett (2007) for an early overview, and for the current state of the art see Kandler and Steele (2012) and recent monographs edited by Bevan and Lake (2013) and Knappett (2013), as well as the other chapters in this book. The main focus of this article concerns the ‘retrodictive ability’ of archaeological models. In the absence of ‘laws’ of human behaviour, there is great freedom in how to proceed.

Networks in Archaeology: Between Scientific Method and Humanistic Metaphor

Running the full gamut of scholarship from physical science to philosophy, archaeology’s diversity can be a negative rather than a positive—when the same phenomena can attract such different approaches that archaeologists end up talking past one another. Take the example of archaeological landscape analysis: on the one hand, this has produced rich, expressive phenomenological studies, and on the other, detailed palaeoenvironmental reconstructions. These two perspectives are not commonly combined, although when they are archaeology emerges as a solid bridge between the humanities and the environmental sciences (van der Leeuw and Redman 2002; Smith et al. 2012). Take another example: artefact studies—on the one hand, poetic, philosophical musings on anything from fabulous artworks to mundane artefacts, and on the other, neutron activation analysis, X-ray diffraction and petrography employed in characterizing stone and ceramic technologies. There are calls (e.g. Jones 2004; Sillar and Tite 2000) to ‘humanise’ the science (and vice versa would also be fitting), and perhaps in artefact studies the integration of the sciences and humanities has had more success than in landscape studies. It is a difficult balancing act. But those archaeological studies that do find a way to combine both often create more convincing interpretations. Alongside landscape and artefact studies, network analysis is a third exemplar of this tension between scientific and humanistic understandings in archaeology. On the one hand, networks can be used quite formally and quantitatively to analyse interactions in space or, indeed, cultural evolution over time (Henrich and Broesch 2011). This use of networks is quite different from a more qualitative, figurative use, as seen recently in book-length treatments by Irad Malkin (2011) and Ian Hodder (2012). There is a danger of the gap between these different understandings of networks widening, just as the humanistic and scientific understandings of both landscapes and artefacts can sometimes seem incommensurate. I think one can see a certain reticence about being sucked into the ‘scientism’ of networks, what one might even dub ‘networkitis’, along the lines of ‘Darwinitis’ or the tendency for all manner of cultural phenomena to now find ‘explanation’ through evolutionary models, and recently the subject of a stinging critique by Raymond Tallis (2011).

How Reliable are Centrality Measures for Data Collected from Fragmentary and Heterogeneous Historical Sources? A Case Study

In social network analysis, centrality measures are used to translate empirical and common sense observations of social behaviour into mathematical expressions. In order to assess how well an algorithm performs in conditions of imperfect data, researchers typically first select either a random or a realworld network, compute a variety of centrality measures, and declare these values to be their point of reference. In a second step, they manipulate these referential networks by adding or removing nodes or ties, again either randomly or following a set of rules. They then compare the centrality measures of the referential network to the ones gathered from the manipulated network. Borgatti et al. (2006) used this approach on a large number of randomly generated networks and found that as long as manipulations were minor (c.10 per cent), results remained reasonably similar to the referential networks’ measures. This approach helps to shed light on the impact of false and missing data on centrality computations, and also helps us to assess the ability of these algorithms to describe social reality (as we reconstruct it) itself. It is surprising that the effectiveness of centrality measures to accurately describe notoriously vague concepts such as ‘power’ or ‘influence’ has not been used alongside empirical observations more often (similarly: Zemljič and Hlebec 2005: 74). In this chapter, I will compare the performance of common centrality measures with the results of an in-depth reconstruction of six historical networks: in this case, support networks for persecuted Jews during the Second World War. Data were extracted from historical narratives, contemporary and retrospective autobiographical reports, interviews, applications for remuneration, and police interrogations. These sources provide a high level of detailed contextual information about the respective ties and actions they represent. It has now become common knowledge that a small minority of Jews managed to survive the Holocaust in hiding and with support from a small and diverse group of helpers. Soon after the end of the Second World War, historians, sociologists, (social) psychologists, and scholars from many other disciplines began to analyse stories of help and survival and found several answers to what seemed to be the key question: ‘Why did helpers decide to help?’

Which Network Model Should I Use? Towards a Quantitative Comparison of Spatial Network Models in Archaeology

Archaeology can be ‘site centric’. Much of the primary evidence comes from excavations based on a single site so naturally the primary sources for archaeological information are organized by site. This is a great help when establishing intra-site links, be they local spatial relationships which may help reveal functions of buildings on a site, or temporal ones, perhaps how different institutions waxed and waned within a society. However, this organization of the primary evidence inhibits comparisons between sites. The regional and global interactions of each site must be deduced by secondary work, comparing information from a range of primary sources with their differing protocols. Yet deducing these wider relationships from finds is one of the key goals of archaeological research as only by understanding societies at all scales can we get a proper view of how society functions. In this sense, archaeologists, and social science in general, have long appreciated that societies are complex systems, with some coherent large-scale phenomena emerging from microscopic interaction, a language that physical scientists have only articulated over the last couple of decades; for example, see Ball (2004) or Lane et al. (2009). Archaeology meets this challenge with several well-developed approaches. Some are rooted in physical science, such as through the chemical analysis of materials. Others are the product of human expertise, as when styles of product are compared across sites. There are efforts to produce secondary regional catalogues through human analysis of the primary sources, for instance see Mills et al. (2013), Sindbæk (2007), Terrell (2010) and chapter 4 of this volume (Peeples et al. 2016) for recent examples. Yet, there remain limitations. Chemical analysis may reveal the sources of materials but not the paths used for their transfer. Stylistic analysis may be subject to unquantifiable bias. A systematic database from primary sources may be too costly to construct. Even with such a database, there is then too much information and we have to pull out the key patterns, to simplify the information into the important parts in order for us to understand what the data is telling us.

Analytical Challenges for the Application of Social Network Analysis in Archaeology

As the chapters and citations in this volume attest, applications of network analytical techniques using archaeological data have a great deal of potential for both addressing traditional archaeological questions and for providing new directions for archaeological research. Importantly, however, many of the network models and methods imported from other fields that are currently gaining popularity within archaeology (see Brughmans 2013) have not yet been fully assessed in relation to the unique strengths and constraints of archaeological data. We argue that archaeological applications of network analyses necessitate particularly careful consideration of the nature of the data included and the applicability of network metrics, many of which were designed with quite different time-scales and levels of certainty in mind. We further argue that, if archaeologists are able to overcome such challenges, the opportunities afforded by archaeological data (e.g. long-term perspectives, material perspectives) will allow us to contribute substantially to broader interdisciplinary discussions of network methodology, interpretation, and theory. In this chapter, we explore four general challenges facing archaeologists applying formal network methods: (1) the use of artefacts to construct network relations; (2) temporal variation among the units of analysis; (3) the definition of network boundaries; and (4) the impact of incomplete datasets. We have confronted each of these issues in our own archaeological network analyses focused on prehispanic settlements in the US Southwest. Some challenges are unique to archaeology while others have been extensively discussed in other disciplinary contexts. Following a brief overview of the data and methods that form the basis of our study, we summarize each of these major issues and offer suggestions for how they might be addressed based on our own experiences and analyses. We do not suggest that we cover all or even most of the challenges archaeological network analysts will face. We do, however, offer a framework for assessing other factors that may influence characterizations of archaeological networks and a general approach for tempering interpretations in relation to such factors.

Networks, Homophily, and the Spread of Innovations

The question of how and why innovations spread through populations has been the focus of extensive research in various scientific disciplines over recent decades. Generally, innovation diffusion is defined as the process whereby a few members of a social system initially adopt an innovation, then over time more individuals adopt until all (or most) members have adopted the new idea (e.g. Rogers 2003; Ryan and Gross 1943; Valente 1993). Anthropologists and archaeologists have argued that this process is one of the most important processes in cultural evolution (Richerson et al. 1996) and much work has been devoted to describing and analysing the temporal and spatial patterns of the spread of novel techniques and ideas from a particular source to their present distributions. Classic case studies include the spread of agricultural inventions such as hybrid corn (e.g. Griliches 1957; Ryan and Gross 1943), the spread of historic gravestone motifs in New England (Dethlefsen and Deetz 1966; Scholnick 2012), and the spread of bow and arrow technology (Bettinger and Eerkins 1999). (For a more comprehensive list see Rogers and Shoemaker (1971) who reviewed 1,500 studies of innovation diffusion.) Interestingly, the temporal diffusion dynamic in almost all case studies is characterized by an S-shaped diffusion curve describing the fraction of the population which has adopted the innovation at a certain point in time. Similarly, the spatial dynamics tend to resemble travelling wave-like patterns (see Steele 2009 for examples). The basic puzzle posed by innovation diffusion is the observed lag between an innovation’s first appearance and its general acceptance within a population (Young 2009). In other words, what are the individual-level mechanisms that give rise to the observed population-level pattern? Again, scientific fields as diverse as economics/marketing science (e.g. Bass 1969; Van den Bulte and Stremersch 2004; Young 2009), geography (e.g. Hägerstrand 1967), or social science (e.g. Henrich 2001; Steele 2009; Valente 1996; Watts 2002) offer interesting insights into this question without reaching a consensus about the general nature of individual adoption decisions. In archaeological and anthropological applications, population-level patterns inferred from the archaeological record, such as adoption curves, are often the only direct evidence about past cultural traditions (Shennan 2011).

Networks or Work-nets? Actor-Network Theory and Multiple Social Topologies in the Production of Roman Terra Sigillata

This paper has a threefold aim: to clarify some misunderstandings concerning so-called ‘actor–network theory’ (ANT), to show how ANT can be put to use in archaeology, and to articulate differences from, overlaps, and possible combinations with ‘conventional’ network analysis. The key argument is that whereas networks imply direct and untransformed flows between bounded entities, ANT renders visible the heterogeneous ‘work-nets’ needed to support and stabilize these networks and the entities they connect. Moreover, networks are only one constellation or social topology that can emerge from such worknets, and we thus need to be cautious not to project properties of networks onto other constellations. Finally, ANT introduces a much-needed dynamic approach in which stability and uniformity of categories and flows is the outcome of contingent processes of maintenance work, and not the starting point. This has important consequences for how we conceive of material culture, and hence of our data, in archaeology: archaeological network analysis tends to assume stable, invariable, and comparable things, traits, or properties. One extreme example of this tendency is so-called terra sigillata, a type of Roman pottery that is so easily recognizable and so well-studied that its stability and invariability across contexts and practices is, to a large extent, taken for granted. The problem is that the starting position of sigillata as a category already posits a particular, non-neutral social topology, with certain possibilities for action. By analysing changes and continuities in the practices by which this type of pottery was produced in a single site in central France, however, this paper will explore some of the problems with this assumption, and suggest ways of resolving these issues. Networks. What’s in a word? Following the recent buzz around networks in everyday and academic vocabulary, the answer seems to veer from ‘everything’ to ‘nothing’ and back. Stretched from a lightweight intuition to deepseated theoretical and methodological axioms, the term risks losing all real potential. Cynics are quick to warn that any discipline, theory, or method flying the banner of networks is amalgamated into a melting pot in which implicit, incompatible, or conflicting principles are stirred.