Linking Up Bell Beakers in the Iberian Peninsula

Many studies in complexity theory employ agent-based models whose interactions can be expressed as networks. In such models, the pattern of interactions between actors is crucial, and the network topology that emerges from the raw data can be characterized through many metrics. One tool previously used in archaeology studies has the potential to deal with networks in social contexts at different scales of analysis: social network analysis (SNA). This discipline has been applied successfully in a wide range of archaeological problems, providing valuable insights and a different perspective. It also could be helpful to quantify concepts associated with social complexity, such as robustness or resilience. In this work, we propose some methodologic possibilities for consideration in the phase definition of the adaptive cycle model (ACM), using SNA tools. To illustrate the process, we will present a case study from the Copper Age in the Iberian Peninsula: the Bell Beaker phase.


Introduction
Social complexity has been a subject of study in archaeology for a long time.The complex systems approach offers excellent potential to deal with social change and linkages between individual actors and society-level features.However, complex systems approaches have not yet coalesced into a homogeneous theoretical framework (Barton, 2014).From a general complex systems perspective, all human societies are complex systems, no matter how broad their structures are (Miller & Page, 2007;Mitchell, 2009).Human societies have been considered systems connected by flows of exchange, material, energy, and ideas, by many research traditions (Flannery, 1986;Moran, 1990;Rappaport, 1971).Complexity theory is Linking Up Bell Beakers in the Iberian Peninsula a general theory made up of a related group of concepts and tools that focus on the effect of parts interacting on the system as a whole.From a broader perspective, complex systems are assemblages of interconnected agents that belong to the same system.Complex adaptive systems (CAS) are a class of these open systems.Human societies can also be characterized as CAS, and there are many examples of application in the field of archaeology (Bentley & Maschner, 2003;Bernabeu et al., 2012;Feinman, 2011).The components of CAS are organized in hierarchical groups that can be represented through the network science paradigm.It also includes some tools that may be of interest for formalizing complex systems in the form of networks.These include inference and the structural characterization of networks.This discipline assumes that its underlying structure contains information about its behavior which can be quantified through certain metrics (Bianconi, 2018).Of all the tools provided by network science, there is one that includes both the networks and the social perspective required for archaeological studies: social network analysis (SNA).This study aims to present a case study illustrating some new views for SNA in providing an approach to quantifying the phases proposed by the ACM in Resilience Theory (Holling and Gunderson, 2002).It will focus on the evolution of social complexity derived from networks of interaction, especially those shaped by the emerging local elites, during the Bell Beaker period in eastern Iberia.This period represents one of the most compelling examples of a cultural phenomenon associated with information circulation through social networks in late European prehistory.At the same time, it also poses many unanswered questions about its origins, spread, and further development (Lemercier, 2018), which will be addressed in this study.

Social Network Analysis
SNA methodology stands out from all the available tools used to quantify social phenomena across long diachronic series, due to its vast battery of metrics to measure them.The study of relational networks created in the past has recently been placed under the spotlight and has been the subject of growing interest among archaeologists (Knappett, 2011;Brughmans, 2013;Van den Berg, 2014;Collar et al., 2015).The implementation of a complex networks perspective in archaeological research has made significant breakthroughs possible in the knowledge of social dynamics from the Palaeolithic to the Middle Ages (Collar, 2007;Sindbaek, 2007;Coward, 2010;Brughmans et al., 2015;Gjesfjeld, 2015;Bernabeu et al., 2017b).Network methods have been successfully applied to various archaeological questions ranging from the spread of ideas to the movement of peoples and artifacts (Bernabeu et al., 2017a;Brughmans & Poblome, 2012;Knappett et al., 2008;Welsch & Terrell, 1998).Despite the different approaches, a common thread can be traced: all of them are focused on analyzing relationships between entities and the emergent patterns that can be recognized.These relationships are present in every single layer of human societies and exert their influence upon individuals, shaping the fabric in which information and artifacts flow.Network models typically consider the network structure and its impact on the agents in enabling or constraining individual action, or the transfer of resources (Wasserman & Faust, 1994).Many studies of social networks have focused on specifying the principles of exchange and power that apply to different network structures (Cook & Whitmeyer, 1992).
SNA has significant methodological flexibility and epistemological versatility, which enables quantitative and qualitative research.Its analytic techniques can be used to provide insights into many areas of archaeological inquiry related to social environments.Social networks can be analyzed based on individual-level attributes, whole networks, and subgroups within networks.Ontologically, SNA requires an emphasis on the connectivity and interdependence of individuals in a group.SNA can provide researchers with information that may improve our understanding of complex relationships and provide insights.
Furthermore, results may stand alone to answer a research question, or they can be incorporated as variables into statistical models.Both empirical and interpretive inquiry methods have successfully been used when incorporating complexity as a framework (Miller & Page, 2007).
The use of this perspective precludes considering individual entities or the structure separately (Brughmans, 2013), integrating collective behavior and individual agency in the same process (Bentley & Maschner, 2003).Complex networks became a handy tool in archaeology for studying variability in material culture through space and time.This variation is an emerging phenomenon that results from collective-individual interactions.As many studies point out (White, 2013), the material culture associated with archaeological contexts is directly related to the relational context in which they were produced.Connected individuals shape every human society; thus, these social ties constitute social networks, which are emergent phenomena produced by an individual's behavior.As people act as channels for information, they can be used to characterize a social system.However, this statement seems like a big jump; social networks articulate material culture well because technical learning is always placed in social contexts (Boyd & Richerson, 1988;O'Brien & Lyman, 2000;O'Brien & Shennan, 2010).
Moreover, it is essential to point out that social ties exert a great influence on information transmission.We can therefore state that the specific form of the material archaeological record is the subproduct of spatially located systems, information exchange, the communication of innovation, and social learning.Many studies also show that differences in the structure of the networks affect the behavior of real-world systems mediated by them, together with the patterns of material culture (Wobst, 1976).All of this therefore suggests that the structure of interaction may have an observable effect on the patterns of material record variability produced by cultural transmission processes (Bentley & Shennan, 2003;Bernabeu et al., 2017a).This extended battery of metrics can greatly help quantify concepts associated with social complexity, which are very difficult to approach.It also has the potential to help resilience theory (Garmezy, 1985;Holling, 1973;Walker et al., 2002) to characterize the different stages of the ACM (Bollig, 2016;Folke, 2006;Holling & Gunderson, 2002).Although most archaeological studies on resilience use this paradigm theoretically, some new ones demonstrate that it can be tackled from a mathematical 1 3 Linking Up Bell Beakers in the Iberian Peninsula perspective (Gronenborn et al., 2014;Weinelt et al., 2021).In this study, we will also propose some possibilities for approaching concepts associated with the ACM.

Geographic and Chronological Scope
The Bell Beaker phase signals a turning point in the dynamics associated with the Copper Age communities in the eastern Iberian Peninsula.It has been highlighted as the moment when social complexity and demographic growth increased and when social asymmetries started to become evident in the archaeological register; however, little evidence can be found in the material record that points to economic specializations which enable the merging of diverse social groups in complex systems of permanent decision-making structures.Some goods, such as Bell Beaker pottery, appear to be exchanged among a few individuals, suggesting the existence of a prestige-based mechanism channeled through rituals and a symbolic world, which would have been used for local ruling groups to form their relational framework (Garrido-Pena & Rojo-Guerra, 2014;Garrido-Pena, 1996).
As previous studies have pointed out (Bernabeu, 1984;Bernabeu & Martí, 1992;Juan-Cabanilles, 2005), there is little doubt about the clear image of continuity in the archaeological record throughout the fourth millennium cal BC and the first part of the third.Nevertheless, this homogeneity seems to fracture during the Bell Beaker phase.The interpretations provided for this cultural phenomenon are not homogeneous.Different approaches try to shed light on the dynamics of such a process by laying out alternative theoretical proposals based on World-systems Theory and Complex Systems, respectively (López-Padilla, 2006;Bernabeu et al., 2006).The late Neolithic culminates a long period that crystallizes in the fourth millennium BC with increasing social complexity that will lead to the Copper Age.As not all the burials in this period contain Bell Beaker grave goods, we can assume that raw materials and prestige objects circulated among the emerging ruling cliques (Juan-Cabanilles, 2005).This process culminated in the Bell Beaker phenomenon, which signaled an inflection point in the background of the third millennium BC.
The geographic framework comprises the eastern and southeastern Iberian Peninsula (Fig. 1).Archaeological excavations in the area made it one of the best-known in Spain for studying the Copper Age (Bernabeu, 1993;Bernabeu et al., 2018;Molina et al., 2004;Garrido-Pena, 1996;López-Padilla, 2006).The study area is defined by the basins of the Almanzora-Andárax Rivers in the south and the Ebro River in the north.It contains a wide variety of landscapes encompassed by the coastal platform and the ridges of the Iberian and Prebaetic Systems.They shape a terrain characterized by mountainous areas and flat coastal plains connected by valleys that work as natural corridors (Aura-Tortosa et al., 1993).
As the scope of this study is focused on the Bell Beaker phase, the timeframe will be established by the available radiocarbon determinations, all between 2500 and 2050 cal BC.All the evidence shows that from the middle of the fourth millennium cal BC, social groups began to present specific signs of inequality probably deriving from an extensive agricultural model (Pérez-Jordà et al., 2021).In addition, studies of the fauna point to an increase in cattle and the exploitation of associated products such as milk and derivatives (Pérez-Ripoll, 1999).Furthermore, during the Copper Age, the intensity and number of exchange networks increased considerably, especially in the southeastern region (López-Padilla, 2006;Pascual-Benito, 1998).These networks seem to include the transmission of artifacts and the techniques associated with their crafting, and raw materials such as copper (Rovira & Montero, 1994).Evidence from sites such as La Vital (Gandia) (Pérez-Jordá et al., 2011) suggests that copper was imported as a raw material and was processed at the site.Therefore, we can support the existence of a metallurgical horizon before the Bell Beaker phase.
Recent works (Bernabeu et al., 2018) have also highlighted the extraordinary demographic growth occurring at the end of the Neolithic in the Mediterranean region of the Iberian Peninsula, following a settlement pattern in the bottoms of valleys close to watercourses, in which there is a significant correlation between storage pits and habitational spaces (Bernabeu & Orozco, 2014;Jiménez-Puerto et al., 2018).Furthermore, some domestic structures could potentially contain far more resources than were needed (Bernabeu et al., 2006).All of this suggests that part of the surplus production was being hoarded by some community groups, which on the other hand were unable to consolidate their primacy.In addition, we cannot overlook the transformation of ritual and grave goods associated with some burials, evidencing the differentiated consumption capabilities of some segments of the social groups (Oreto García- Puchol et al., 2013).
The material record of the communities on the Mediterranean coast, from Almería in the south to the Júcar River in the north, is very homogeneous, and many Linking Up Bell Beakers in the Iberian Peninsula similarities can be observed (López-Padilla, 2006;Pascual-Benito, 1998).It therefore follows that these social groups could have been part of a more comprehensive relational network in which ideas and objects circulated (Furholt, 2020).Bell Beaker pottery is abundant in the Mediterranean region of the Iberian Peninsula.The so-called international styles shape the first Bell Beaker pottery horizon.From that moment on, an inflection point can be observed in sites such as Los Millares (Almería), beginning a period when large settlements broke up and were replaced by smaller aggregated habitats (Molina et al., 2004(Molina et al., , 2020)).This process, evident at the sites and burials from the same period in Alicante and Valencia, has traditionally been associated with the social disintegration that occurred just before the appearance of the Argaric culture (Jover-Maestre & García-Atienzar, 2014;Lull et al., 2010).During the Bell Beaker period, the predominant funerary ritual in natural cavities continued, but the number of bodies buried fell dramatically, and greater numbers of weapons and exotic raw materials (i.e., barbed and tanged flint arrowheads, copper knives, ivory) are recorded as grave goods.The late part of the Bell Beaker phase has traditionally been associated with a period of crisis, increasing the potential for conflict and cultural fragmentation (López-Padilla, 2006;Lull et al., 2013).It also appears to be a moment that witnessed the contraction of interaction networks, which tend to be limited to increasingly local connections (Lillios et al., 2016).Recently, diffusionist theories have become popular thanks to genetic analyses that point to the arrival of new gene pools in the peninsula (Olalde et al., 2019), although their conclusions are controversial.Furthermore, as many studies have pointed out (Bini et al., 2019;Blanco-González et al., 2018;Hinz et al., 2019), environmental changes must be taken into account as well.This is the case of the paleo-environmental studies highlighting a wide range of climatic events around 4.2 ka.
Nevertheless, the research has come up against significant limitations due to the scarcity of a closed archaeological context for the Bell Beaker phase.Many of these arise from altered environments or earlier excavations with little stratigraphic information (Bernabeu, 1984;Garrido-Pena, 1996;Juan-Cabanilles, 2005) and a considerable absence of short-lived radiocarbon determinations (Ríos et al., 2011).Another difficulty is associated with the calibration curve and the high error margins associated with this period.Defining a chronological framework is therefore a very challenging task.
Be that as it may, despite the growing complexity in the relational sphere, during the third millennium BC, there is little evidence of the existence of economic specialization and interdependencies with the potential to merge diverse social groups into permanent decision-making structures.Some of the items which circulated among a few individuals suggest the validity of mechanisms such as the prestige and the exclusive ideology of the elites, which are probably responsible for the network's development and would be a key variable in the process of increasing complexity that reached its peak at the end of the Bell Beaker phase.It is necessary to make it clear that this only holds true in comparison with the subsequent Bronze Age, but this aspect falls outside of the scope of this study.

Materials and Methods
This study focuses on the Bell Beaker phase and addresses the idea of connectivity through a methodology that is increasingly popular in archaeology: Social Network Analysis (SNA).Previous studies have addressed this issue using a network perspective (Caraglio, 2020;Caraglio et al., 2022;Clarke, 1976;Kleijne, 2019).The ceramic wares associated with the Bell Beaker phenomenon are a marker for a new symbolic world associated with the emerging elites (García- Puchol et al., 2013;Garrido-Pena & Rojo-Guerra, 2014;Garrido-Pena & López-Astilleros, 2000;Lemercier, 2011;Salanova, 2005).The networks needed to perform the analysis will be based on similarity.The variables used to quantify the similarities are defined with stylistic and morpho-technical criteria applied to decorated ceramic wares, creating ad hoc styles.Moreover, a Bayesian classification procedure will be used to provide a chronological framework.These tools together will make it possible to use a relational approach that enables the connection of archaeological information from a wide range of contexts in a large area, and a diachronic axis, following the flow presented in Fig. 2.

Bell Beaker Decorations
There is a long tradition of studying the pottery in this area.Many methodological tools have been developed to analyze every formal aspect (Bernabeu et al., 2011(Bernabeu et al., , 2017b;;Fenyvesi & Lähdesmäki, 2017).The organization of decorations and their relation with symbolic beliefs has been emphasized by many studies (Cunningham, 1973;Washburn et al., 2010;Wilbert, 1993).Bell beaker wares are closely associated with a change in the symbolic world of the emergent Copper Age elites (Bernabeu, 1984;García-Puchol et al., 2013).One of the most remarkable aspects of the Bell Beaker phase is related to its presence in burials, which do not represent all of the community due to the low numbers of associated individuals.That means only a tiny proportion of the group were given such symbolic treatment.The rest were buried in other ways, as evidenced in the Madrid region's much-studied sites (Liesau & Blasco, 2011;Garrido-Pena et al., 2019).The materialization of Bell Beaker pottery in the study area is diverse, and its coexistence with previous funerary practices is evident in many places (Pascual et al., 2005).Together with the decorated vessels, artifacts associated with warfare (copper knives, Palmela arrowheads) can be found.These grave goods are usually related to individuals whose power would be supported by an ideology in which the display of power would be socially appreciated (Salanova, 2005;Lemercier, 2011).This new symbolic paradigm and the decorated ceramic wares are associated with ceremonials in which alcoholic beverages were consumed (Sherrat, 1987;Rojo-Guerra et al., 2008), possibly connecting the world of the living and the dead.The analysis of the information flows that played their part in the spread of Bell Beaker pottery could be extremely helpful when considering the question of the symbolic transformation of Copper Age ruling groups.
Bell Beaker vessels were produced locally, as other studies have pointed out (Barroso et al., 2015;Blasco et al., 2011;García-Puchol et al., 2014); the decorations, however, are highly standardized, primarily the corded and herringbone wares, which are supposed to be the oldest.Nevertheless, stylistic variability is greater among the later ones (incised and incised-stamped), leading us to picture a scenario with different regional groups.This suggests that the transmission of information between the communities was more homogeneous in the first part of the Bell Beaker phase, connecting vast geographic regions.This situation, however, breaks down in the latter part, resulting in a fragmented panorama.This circumstance makes decoration a pivotal aspect for analyzing the transmission/diffusion of information at a macro scale.
The decorative patterns of Bell Beaker pottery present some problems.Chronological attribution of the main decorative styles is one of them (Bailly & Salanova, 1999;Salanova, 2005).Despite the spectacular findings at many sites with radiocarbon determinations on short-lived samples (Humanejos, Camino de las Yeseras, Túmulo de la Sima or La Vital), the mixture of vessels decorated in different styles in the same context makes it difficult to get a clear idea.The difficulties associated with the calibration curve must also be mentioned.The existence of a long distribution plateau for this period introduces a significant factor of uncertainty in the equation.In addition, the interpretation of the Bell Beaker phase is far from complete.The ceramic wares are the visible part of a wide range of events framed in the context of migrations, the circulation of artifacts, and the transmission of ideas.The origins of this phenomenon, its accurate dating, and the axis of its diffusion are yet to be determined.Moreover, there are also many questions about its impact on the regional development of the earlier late Neolithic cultural groups (Lemercier, 2002).Finally, another question must be answered concerning the late Bell Beaker period and the transition to the Bronze Age.
The sample comprises exclusively Bell Beaker decorated ceramics.The sample (Jiménez-Puerto & Bernabeu, 2023) is a subset of a larger open-access database (Jiménez-Puerto, 2022b), and it contains information from 99 archaeological contexts.The Bell Beaker vessels included were all complete enough to consider the techniques used to decorate them.Small fragments and those that did not provide suitable information were ruled out.As the Jaccard index has been calculated, the final information was limited to the presence-absence of the studied decorative types in each archaeological level.The sample has been organized by considering the following criteria.The first layer of the classification uses functional and morphologic criteria.It separates the sample into two categories, vessels and bowls-pots, but only those that allow an almost complete reconstruction of the decoration have been considered.These two groups were formed because they seem to appear in the archaeological record for different reasons.On one hand, the vessels are found mainly in funerary contexts and seem to appear earlier.
On the other hand, bowls and pots appear later, found in both habitat and burial contexts.In addition, so-called International decorations are absent from bowls and pots, which tend to present late-fashion compositions.The second layer of the classification focuses on the techniques used to decorate the pottery (Fig. 3).The main techniques are as follows: • Corded: composed of horizontal lines made from cord stamps.
• Stamped: a stamp made with a gradine.Decorative patterns are usually formed of horizontal motifs, but there are many variants.• Stamped short-lined: a stamp shaped like a short stroke.It is performed with a tool with a short edge.It is always found in combination with other techniques, like incised.• Stamped polygon shaped: it is defined by the use of a tool with a polygonal edge to make the stamps.It is always found in combination with other styles.It is widespread in the regional styles, characteristic of the late Bell Beaker period.• Incised: Incision made with a pointed tool.
• Ungulated: a pinch made with the fingertips.It is rare but is always found with other Bell Beaker wares associated with the early phases, and it has probably gone unnoticed in many assemblages.
It is essential to mention that these techniques can also be found combined.Not all the associations of techniques are present, though.Some categories have been constructed, grouping all the possible combinations together in the two main forms, vessels and bowls-pots (Table 1).Additionally, some of them have a clear chronologic value.That is the case of E1 and E2, which are found mainly in regional styles such as Ciempozuelos, traditionally associated with late Bell Beaker contexts.

3
Linking Up Bell Beakers in the Iberian Peninsula

Bell Beaker Techniques Phase Modeling
As previously stated, the chronology of Bell Beaker wares is problematic and presents a series of issues as yet unresolved.To make the temporal framework as accurate as possible, we propose a chronological phase model with the Bayesian chronological modeling tool Chronomodel (Lanos & Philippe, 2018).It will enable us to create a framework in which to carry out the chronological attribution of the archaeological contexts dealt with in this study.As an organizational basis for the model,  we have used the technical categories previously commented on, and the available 14 C short-lived determinations for the study area have been used.We have made sure all of them come from closed contexts and short-lived samples to minimize the uncertainty; however, it is necessary to add some determinations from areas that are not included in the study to ensure that some techniques are represented properly (Table 2).Many combinations have been tried, and finally the most statistically robust one includes three successive periods.These periods have been defined by the stylistic and stratigraphic criteria suggested by the academic literature (Harrison, 1977;Bernabeu, 1984;Garrido-Pena, 2000;Rojo-Guerra et al., 2005).It is essential to mention that the techniques are usually found combined, so the most common combinations have been taken to define the periods.The only technique excluded from the model is corded ware because it lacks 14 C short-lived determinations.It has however been associated with early Bell Beaker periods according to stratigraphic criteria (Suarez-Otero, 1996).The model proposes phase delimitations that can be followed in Fig. 4. As can be seen, the two horizons (first and third periods) do not overlap and are easy to distinguish.That is not the case in the second period, which overlaps with both the first and the third, acting as a transitional phase, which is sometimes difficult to detect.The first period corresponds to the stamped techniques traditionally associated with the so-called international styles, corded, gradine-corded, and ungulated.They are followed by a combination of stamped plus incised-stamped wares.Finally, the late productions are characterized by combinations of incisedstamped decorations.
The resulting model is consistent with the findings provided by stratigraphy and will be used to perform the Bayesian Chronological attribution of all the contexts with no 14 C determination, as discussed in the next chapter.It should also be noted that period 2 overlaps with periods 1 and 3, which are the ones that represent chronologically distinct moments.

Bayesian Attribution
All the archaeological contexts with information from artifacts but no absolute chronology have been processed using a novel procedure that has been tested and published recently (Pardo-Gordó et al., 2022).This procedure associates any archaeological level with a previously defined period.We used our chronological phase model to represent our periods or windows (Fig. 4).Each period will be characterized through the artifacts in contexts with absolute short-lived radiocarbon determination, confirming the so-called a priori (Table 3).The automatic Bayesian method is based on the Dirichlet-multinomial inferential process (Alvares et al., 2018), which uses the a priori information to predict the periods associated with a particular artifact assemblage.
Once the periods are characterized, the multinomial classifier proposes a graph for each level in which we can find an estimation of probability for each window.Although there are clear situations, it is necessary to define a threshold value for all those that are not, together with some rules to apply when uncertain.In this case, 1 3 Linking Up Bell Beakers in the Iberian Peninsula   we have set a threshold of 0.25 to accept a prediction (Fig. 5-A), rejecting those not reaching it (C).The threshold value selection follows no specific statistical criterion and we have followed the recommendations of the creators of the method (Pardo-Gordó et al., 2022).When the results are not conclusive, they are compared with the information provided by stratigraphy and the associated material record, which was extracted from the available excavation reports, publications and monographic articles.In most of the cases the procedure was satisfactory, but there were a few cases in which there was no clear attribution, such as the bimodal distributions.All the bimodal distributions have finally been discarded (D).Also, when a period reaches 0.75, all the others are ruled out regardless of their probability (B).

Networks
Once each context has its chronological attribution, the next step is the composition of the similarity networks that are used to perform the SNA.It is necessary to convert the archaeological into relational matrices.The similarity coefficient used to conduct that study is the Jaccard (Jaccard, 1912;Liu et al., 2016) as it does not take into account the absolute frequencies in the calculation, but it does the presenceabsence of each item, in order to avoid biases produced by collections with many items (Jiménez-Puerto, 2018).The Jaccard coefficient also needs to be normalized to compensate for the variability between the chronological windows with few variables present, so we have used the formula proposed in previous studies (Bernabeu et al., 2017a).Another issue that must be addressed is that similarity networks tend to present high link densities because any similarity between two nodes generates a link between them, no matter how small it is, something that usually introduces noise in the subsequent analyses.A usual practice to avoid this problem is to apply mechanisms such as thresholds.In this study a threshold of 0.25 was used.
Finally, the networks have been arranged according to their geographical situation, using the Gephi application (Bastian et al., 2009;Jacomy, 2011).Once composed of the networks corresponding to each window, some metrics have been analyzed to determine the diachronic evolution.In this network application, we have applied some available metrics and tools to trace diachronic development through the different windows.We have focused on the betweenness centrality measure, which provides an idea of the role played by each actor in the information flow, allowing us to detect bottlenecks.It has the potential to help in the characterization of the network's topology, enabling the detection of situations in which the structure is sensitive to perturbations in the information flow (Barthelemy, 2004) or potential edge-of-chaos situations (Kanders et al., 2017;Langton, 1990), which compromise the robustness of the network.Robustness is the ability to withstand failures and perturbations and is a critical attribute of complex networks (Qin et al., 2013).If robustness is low, the network flow has a higher risk of collapse.The breakdown of a complex network happens abruptly during a phase transition at some critical fraction of nodes removed (Cohen et al., 2000), and its threshold changes from one topology to another.For example, scale-free distributions are resilient to attacks that knock out nodes randomly but are vulnerable to targeted attacks on the hubs.We have done a robustness test for all three periods to clarify this point.Finally, we have implemented some different community detection analyses to contrast the results: Girvan-Newman (Despalatović et al., 2014;Girvan & Newman, 2002) and statistical inference (Zhang & Peixoto, 2020).The nature of large, interconnected networks makes it practically impossible to detect the underlying communities manually.Although these networks are not big enough to make inspection impossible, the methods enable the intersubjective reproducibility of the results.In this context, community detection algorithms are used to find groups of densely connected components inside the network, which share a common background.

Results
The network graphs composed taking into account the techniques associated with the decorations (Table 1) allow us to observe the changes in the distribution of the main shapes-techniques.Although Bell Beaker pottery reached the Iberian Peninsula circa 2550 cal BC, its presence is not confirmed until 2500 cal BC.The decorated wares corresponding to Bell Beaker international styles can be found around the studied area in the first period.Each node represents a context belonging to an archaeological site.All of them have been arranged according to their geographic location using the Gephi plugin Geolayout (Jacomy, 2011), so the networks contain a geographic component. .The color of each node represents its degree.Light shades indicate a lower number than dark ones.The size signifies the betweenness centrality of each node: the bigger the node, the more significant the value.The intensity of the link between two nodes indicates the weight; the more intense, the heavier.
We have assumed that all the sites present at a specific window are contemporaneous.However, this may not always be the case.As discussed in the conclusions, the definition of the available radiocarbon series placed a limitation on this study, something that will need to be addressed in future studies.Furthermore, the chronologic overlapping of the second and first periods must be discussed.The low chronologic definition of period 2 seems to be related mainly to its characterization, which comes from only one site (Humanejos).The results, however, are consistent with the material culture associated with the period.These correspondences remind us that the second period acts as a transition between the early Bell Beaker period and its homogeneous styles and the late period with the heterogeneous regional types (Bernabeu, 1984;Juan-Cabanilles, 2005).The nearly equal duration provided by the chronological model for the first and third periods reinforces this impression.The SNA is focused on some metrics, such as density, clustering, and average path Linking Up Bell Beakers in the Iberian Peninsula length, as shown in Table 4. Interestingly, density values increase monotonically throughout the period, despite the strong variations in network size.
The first period (c.2450-2340 cal BC) (Fig. 6) clearly shows a connected world.The external nodes present higher betweenness values, together with the Serpis Valley region.Note that a high betweenness value can point to a central node or an actor that plays a frontier role in the network (Barthelemy, 2004).This suggests a world in which the different clusters are well connected.The central and southern coastal regions (south of the Júcar River) are densely connected, and sites such as Los Millares-Ciavieja play a significant betweenness role.Additionally, a not-so-dense cluster can be found to the north of the Turia River that reaches the mouth of the Ebro River.Furthermore, the central valleys (Júcar, Ebro, Turia) and Almansa corridor connect the littoral with the Meseta and Tajo basins.However, the links show lesser intensity than those connecting the coastal regions.
The second period (c.2408-2261 cal BC) (Fig. 7) acts as a pivot and shows symptoms of disintegration.Generally speaking, the intensity of contacts is reduced in all areas.Nevertheless, the area south of the Júcar River maintains its inner connectivity, and the Los Millares site still plays a significant betweenness role.The regions to the north, especially the Ebro basin, seem to cease exerting their influence on the southern sphere, although they maintain a slight connection with the central area.
In the third period (c.2313-2197 cal BC) (Fig. 8), the southeastern sphere loses much of its influence over the network.On the contrary, the connections between the central coastal area, the Tajo headwaters, and the Iberian System mountains increase dramatically, now playing an increased betweenness role.In general, most nodes' Fig. 7 Graph visualization of the networks corresponding to the nodes of the second period.The size indicates the betweenness centrality.The small window on the right shows the links betweenness values are lower than in previous periods, something that reflects more distributed networks.This is a symptom of increased robustness and a certain degree of recovery.However, the average strength of the links is lower than in previous windows, which could be interpreted as a symptom of weakened information flows, enabling the appearance of local stylistic dissimilarities.The connections with the Ebro River appear to increase, but using the new route through the mountains of the Iberian System, marking the initial moment of the heterogeneous regional Bell Beaker styles, which tend to be associated with a more culturally fragmented world.
On one hand, the average betweenness presents a descending trajectory along the series.The average betweenness for the three periods is 0.038 for period 1, 0.043 for period 2, and 0.007 for period 3.The decreasing trend across the different windows can be related to many variables.For instance, the density increase (Table 4) might underlie the reduction of the betweenness detected.One interpretation that matches the archaeological record and the observations well points to an overall increase of links that could undermine the betweenness of specific bridging nodes in window 3, thus reducing the average betweenness.This could be considered an expression of the progressive small-world tendency that creates densely connected groups with weak ties to other communities, but this possibility will be further explored later.
Individual average betweenness seems to follow an exponential distribution in windows 1 and 2 and is unclear in 3 (Fig. 9).The maximum particular concentration can be found in window 2, together with the higher exponents, and occurs at the Los Millares and La Pedrera sites (which account for 50% of the total betweenness for that window).On the contrary, window 3 does not appear to follow an exponential Linking Up Bell Beakers in the Iberian Peninsula distribution.That could be interpreted as the moment in which the tendency to develop scale-free networks is broken (Broido & Clauset, 2019), leading to a more distributed system, on the verge of the Bronze Age, but the reasons are still unclear.
Could this be caused by the concentration limit being exceeded?This limit of concentration could indicate an edge-of-change situation for the network.Is there any way of quantifying the limit for this concentration that could signal a turning point or a state shift?What are the reasons that drive these situations?All these questions must be addressed in upcoming research.
Further analysis will be conducted to get new perspectives and confirm the initial hypothesis: the existence of a highly connected and homogeneous world in the first period and a culturally fragmented one in the last.First, we have compared the network metrics of average path length and clustering to check the possibility of small-world situations (Watts & Strogatz, 1998).Figure 10 shows that the period with the greatest chance of a small-world structure is the third due to its high clustering and a lower average path length (Albert & Barabási, 2002).
In window 1, the clustering is high, but the average path length is high also, so we cannot speak of a small-world situation.Window 2 clustering reduction  clearly shows this period's transitional role.The small-world status for window 3 means that very densely connected entities are related to other clusters through weak ties.The Fruchterman Reingold layout (Fruchterman & Reingold, 1991) illustrates this situation.In Fig. 11, the difference can be seen between periods 1 and 3 and the small-world effect for period 3.The color indicates the community, and the size shows the betweenness.Clusters refer to highly connected entities that have a lesser between-group connection.This comparison shows that the information flow becomes far more evenly distributed and much less centralized over time.Periods 1 and 2 show far more scale-free networks than period 3 (Figs.9 and 12).Clearly there is a breakdown of a hierarchical system visible in periods 1 and 2, leading to a more distributed smallworld network in period 3.In addition, we have used different community detection analyses to contrast the results: Girvan-Newman (Despalatović et al., 2014; Girvan  Linking Up Bell Beakers in the Iberian Peninsula & Newman, 2002) and statistical inference (Zhang & Peixoto, 2020).As can be seen in Table 5, the different algorithms find a similar number of communities across the three periods.We have employed these algorithms to quantify the communities present, not to detect geographical or cultural groups.According to the results, period one would be the most homogeneous due to the few communities found.The second period witnesses a noticeable increase in the clusters found; the third period clearly shows more significant fragmentation, illustrated by many clusters.It is necessary to point out that, as shown in Fig. 11, the network in window 3 is divided into two main groups connected by a third, playing a linking role.In period 1, the nodes connect the network with a higher betweenness centrality value.The connectivity in this period is dependent on these bottlenecks, which means that the network's topology could be linked to hierarchical topologies, as can also be seen in the metrics of Fig. 10.To quantify this extent, we have carried out a twofold robustness test.On one hand, we have conducted a robustness analysis of the three networks, which involves attacking them by removing nodes.This procedure has been implemented with Python (Van Rossum & Drake, 2009) and the networkX-robustness package (Santanam, 2023).The attacks include random attacks and targeted attacks on nodes with the highest degree of centrality and betweenness centrality.Attack functions return the initial fraction of nodes in the giant component, the fraction of nodes in the giant component, and the average path length in the giant component after each node removal.By observing how the average path length changes as nodes are removed during an attack, we can gain insights into how resilient the network is to such attacks.If the average path length remains relatively stable even after significant node removal, it indicates that the network is more robust and able to maintain efficient communication pathways.A smaller average path length indicates that nodes in the network are more closely connected, allowing for efficient communication and information dissemination.On the other hand, a larger average path length suggests that the network becomes less efficient in transmitting information due to increased distances between nodes (Newman, 2012).We have also calculated the Molloy-Reed criterion (Cohen et al., 2000), that helps determine the robustness of a network to complement the other metrics involved.It is based on the concept of degree distribution, which represents the frequency of nodes with different degrees.The Molloy-Reed criterion compares the actual degree distribution of a network to a random network with the same number of nodes and edges.If the network has a lower degree distribution than the random network, it suggests that the network is more vulnerable to attacks and failures.If the differences between the values of Molloy-Reed are large, it suggests that the networks or scenarios differ significantly in terms of robustness.The results can be followed in the new Fig.12.The results corresponding to a random attack are clearly different for window 3, but those of the attack based on betweenness centrality are more similar in windows 2 and 3, which remain stable until 35% of the nodes are removed, than in window 1, which starts to collapse at the 20% mark.This clearly shows that window 1 is behaving as a scale-free network that is highly vulnerable to attacks on key nodes.On the contrary, windows 2 and 3 behave better when nodes with high betweenness are eliminated.This is confirmed by the Molloy-Reed criterion, which stays quite stable in windows 1 and 2, but increases dramatically in window 3, as can also be seen in Fig. 12.
In addition, we have performed a robustness test by applying successive edge weight filtering.The results show that the connectedness of the network corresponding to period 1 is more robust than the other two.We have manually removed 40% of the link weight for all periods using Gephi filtering tools.While 63.27% of the Period 1 network structure remains visible, only 21.08% of period 2 and 21.88% of period 3 do.It is a clear sign of the higher robustness of period 1 connections, which is also consistent with the homogeneity of the material record of the early Bell Beaker phase.These results are consistent with our initial premises and point to a crisis beginning in period 2 that lasts until period 3, despite the growth of the network.We have a first period with a more homogeneous culture and a third period characterized by a fragmented world with a small-world effect.

3
Linking Up Bell Beakers in the Iberian Peninsula

Discussion and Conclusions
All the evidence obtained from the analysis in this work points to the existence of two different periods in the Bell Beaker phase: the first period, in which the decorated vessels reached the Iberian Peninsula with remarkable homogeneity in all areas, and a late moment in which uniformity gave way to a culturally fragmented phase that ended with the Bronze Age.However, despite the climatic event known as the 4.2K (Bini et al., 2019;Hinz et al., 2019;Weinelt et al., 2021) and the evidence of cultural regionalization in the Mediterranean area (Bernabeu & Martí, 1992;Bernabeu, 1984;Garrido-Pena, 1996;Juan-Cabanilles, 2005), it must be noted that recent studies have pointed to sustained demographic growth by the end of the Bell Beaker phase for the study area (Balsera, 2017;J. Bernabeu et al., 2018;Blanco-González et al., 2018).This situation is confirmed by our networks, whose size acts as a demographic proxy for the networks in SNA, noting a slight increase between the first and the third period, which is supposed to be a crisis moment.Looking at the networks in Fig. 12 and the distribution of betweenness in Fig. 9, it becomes clear that periods 1 and 2 have a scale-free distribution, which is especially vulnerable to the failure of crucial nodes that dominate the network structure.
In contrast, phase 3 is much less steeply distributed and can thus be equated far more with a small-world network, as the metrics showed.To summarize, for phase 1, we recognize a hierarchical network with predominant nodes; phase 2 still represents a hierarchical network, but one in which interconnectedness generally decreases significantly and represents an inflection point, and phase 3 forms a significantly less hierarchical network.According to the data considered, the crisis should thus be placed in phase 2, coinciding with the abovementioned 4.2K event, although it must be noted that the chronological resolution for this period is lower than for the other two.All these facts, together with the small-world situation detected in period 3, lead us to think about the last period and its culturally fragmented panorama in a different way.The period prior to the Bell Beaker phase was one of homogeneity in the area studied, as has been evidenced by previous SNA studies (Jiménez-Puerto, 2022a).Thus, period 1 represents a continuation of the dynamics from earlier moments.The resilience and metrics analyzed point to the consideration of period 1 (Fig. 13) as a moment of exploitation or growth (r-K) in which the emerging local elites embraced the Bell Beaker phenomenon as a way of justifying their rising position.In period 2, the information networks show a moment of crisis, clearly corresponding to a dissolution moment (Ω), whose causes are not clear but could be related to the climatic situation.On the other hand, period 3 represents a moment of continuation of the crisis, which seems to be unrelated to subsistence because the network clearly grows.Although the information does not flow as easily as in period 1, some signs of recovery can be seen in the metrics, and the small-world situation detected confirms this, so we consider this period to be a phase of reorganization (r).The causes of this regionalization seem to be the product of the internal dynamics of the system.The heterogeneity and abundance of decorated wares in this phase can be associated with a "democratization" of the Bell Beaker phenomenon, possibly associated with emulation.External causes cannot be ruled out either, however, due to the complexity of the situation for the Iberian Peninsula on the verge of the Bronze Age.
Recent studies on the development of exchange networks in the area during the transition to the Bronze Age have concluded that the flow of copper artifacts, far from declining, becomes more robust in the last period of the Bell Beaker phase (Jiménez-Puerto, 2022a).Recently, new genetic studies have added yet another dimension to this rather indistinct picture, proposing the appearance of new peoples coming from the Eurasian steppes (Olalde et al., 2019;Villalba-Mouco et al., 2021).All this research suggests that events taking place in the Bell Beaker phase and the transition to the Bronze Age were far more convoluted and complex than expected.Therefore, to properly assess the definition and impact of the Bell Beaker phenomenon, it would be necessary to increase the breadth of the chronological framework.That means including the periods just before and after its appearance and development in the analysis to get a more accurate background picture.
Finally, some habitation sites in which these decorated wares are absent share the same Bell Beaker chronology.This is especially true during the early phase, where the Bell Beaker phenomenon seems more related to the funerary world.Another approach should be tested to compensate for all these possible deviations, combining graves and habitats in the same model to enhance their fusion into new network nodes.
Our initial aim in this study was to propose an approach to ACM phase definition through SNA.Based on the metrics provided by SNA, we have proposed a phase definition explained in Fig. 12.Our proposal of using SNA in combination with Resilience Theory is still in its early stages, and future studies, which will attempt to refine this first approach, are still in progress.Consequently, some research lines are explored.One of the biggest challenges in archaeology is determining the relationships between artifacts.Social Network Analysis is a handy tool, with great potential, for dealing with relational information.In this study, we have proposed applying SNA to the problems associated with the Bell Beaker Linking Up Bell Beakers in the Iberian Peninsula phase by analyzing the techniques of the decorated wares.The accuracy of the results has however been limited by some issues, derived mainly from the low resolution of the 14 C series (Crombé & Robinson, 2014;Peros et al., 2010;Surovell et al., 2009).We cannot forget the problems associated with the calibration curve in the period (Michczynski & Michczynska, 2006;Weninger et al., 2015), which introduces a high uncertainty effect.Improving the absolute chronology associated with the Bell Beaker phenomenon should be a top priority for further development.Many more short-lived radiocarbon determinations coming from a closed context are needed to make it possible.
In addition to that, as many existing vessels emerge from altered contexts, another approach could be tested.For such wares, thermoluminescence analysis could be conducted.As it also requires the soils in which the pottery was found to be measured in order to calibrate and increase the accuracy, it should be performed at suitable sites (Arribas et al., 1989;Liritzis et al., 1994).The Cova de les Cendres (Teulada-Moraira, Alacant) provides a perfect context for conducting such an analysis.
Another challenge that must be addressed for SNA studies is related to the contemporaneity of the sites that share a chronological window.The resolution of the available radiocarbon series should be increased to create smaller chronological windows.The smaller size of the windows could improve the correct association of the synchronous sites present at a specific window, enhancing the results.
Although it is difficult, quantifying complexity could be another pathway to be explored in future works.It could help determine edge-of-chaos situations where the system works well and is resilient to disturbances (Carroll & Burton, 2000;Teuscher, 2022).There are some theoretical proposals to quantify complexity in networks, such as Von Neumann entropy (Petz, 2001).New studies suggest that the Kolmogorov complexity index might be a more consistent network method (Morzy et al., 2017), which will be tested in future studies.
In addition, the study of the stylistic features of Bell Beaker decorations should be explored.We are currently working on defining formal styles found on vessels whose complete decoration can be traced.This approach could provide a more accurate idea of the relationships between the different communities since cultural transmission always take place in social contexts (Bentley & Shennan, 2003;White, 2013).
In this study, we have focused on ceramics through the study of decorative techniques, but further analysis of other proxies or artifacts should be conducted.A new SNA would be performed, but using multiplex networks.That would make it possible for multiple layers or networks (metallic, flint arrowheads, ideotechnic artifacts) to be integrated in a single analysis, confirming the results and creating a better picture for quantifying the complex processes of the Copper Age in the Iberian Peninsula.
All of these proposals are being considered in the ongoing Prometeo-Neonets project, in which the authors are involved, where studies are underway to extend the sample through the analysis of publications and materials in the eastern part of the Iberian Peninsula.

Fig. 3
Fig. 3 Main individual techniques that can be found in the decorations Fuente Olmedo

Fig. 5
Fig. 5 Different situations processed by the multinomial classifier.This image comes from a random example with ten periods involved, to make the situations clearer

Fig. 6
Fig. 6 Graph visualization of the networks corresponding to the nodes of the first period.The size indicates the betweenness centrality.The small window on the right shows the links

Fig. 8
Fig. 8 Graph visualization of the networks corresponding to the nodes of the third period.The size indicates the betweenness centrality.The small window on the right shows the links

Fig. 10
Fig. 10 Clustering and average path length (normalized) of the three periods

Fig. 12
Fig. 12Average path length evolution after removal of nodes from the giant component with three different attacks (random, degree, betweenness) for the three windows

Fig. 13
Fig. 13 Adaptive cycle proposal for the Bell Beaker phase in Eastern Iberia

Table 1
The most commonly combined techniques are associated with the main shapes

Table 2
14 C determinations were used for the Bayesian modeling

Table 4
Main structural metrics of the three networks