Abstract
Keywords
[S]cience is disunified, and – against our first intuitions – it is precisely the disunification of science that underpins its strength and stability. (Galison, 1999: 137)
Readers from the field of Science and Technology Studies (STS) have encountered the network, and likely observed how disunified it can be: following Galison’s (1999: 157) metaphor, a laminated mess of “partially independent strata supporting one another”. As we argued in a previous article (Venturini et al., 2019), STS engage with the network in multiple ways. Actor-network theory (ANT) used the network as a metaphor to criticize “notions as diverse as institution, society, [and] nation-state” (Latour, 1999: 15; see also Law, 1999), although post-ANT moved away from networks. More recently, at the intersection of digital media studies and STS, some scholars use the network as a “social science apparatus” (Ruppert et al., 2013), often in a perspective of critical proximity, while reflecting on the network’s pervasive involvement in the infrastructure of datafied society. In this context, like other forms of Big Data, the network’s material-semiotic properties produce data-worlds, for instance, as network maps are interpreted as if they are self-evident (Bounegru et al., 2017; Burrows and Savage, 2014; Marres and Gerlitz, 2016). This movement is critical of Computational Social Science (Lazer et al., 2009), and concerned with the theories and models embodied in network tools (Rieder and Röhle, 2017), and their uses and abuses (Marres, 2012). STS scholars know how problematic the network can be, as the confusion it causes has been documented. Nevertheless, they did not create their own trouble with networks (van Geenen et al., forthcoming); they imported it.
STS scholars tend to presume that the disunification of the network happened when it was repurposed from the exact sciences, where the network was originally unified. But this initial state of unity never existed: The network has always been disputed.
There is no doubt that the
In sociology, Erikson (2013) accounts for a slightly different opposition, between the
The transdisciplinary field network science (NS) emerged in the late 1990s under the joint patronage of social network analysis and the study of complex systems (Barabási, 2016; Borgatti et al., 2009), focusing on a specific type of network: the
In this piece, I follow in the footsteps of Galison (1999) in
After introducing the key concepts of NS, and then my method, I account for the first dispute, in 2005, regarding which statistical distributions characterize complex networks. I analyze its commonly accepted framing as a tension between disciplines, and I explain why the subsequent efforts of multiple authors to defend a position of compromise did not put an end to the controversy. Then I introduce the notions of nomothetic and idiographic approaches to knowledge, and account for the second dispute, in 2018, concerning the experimental procedures capable of assessing the (alleged) pervasiveness of complex networks. Finally, I reframe the second dispute as an epistemic clash between theorists and experimentalists, the latter gradually opposing their own agenda to the former.
Network science is a controversial field
NS is not a firmly delineated discipline but a “highly interdisciplinary research area” (Börner et al., 2007) whose origin is disputed. For Borgatti et al. (2009), NS emanates from the older and well-established field of
Despite these different perspectives, all scholars acknowledge multiple points of origin, and the trouble it causes. Freeman (2008) accounts for two distinct communities within the field, and their mutual influence. Keller (2005, 2007) argues against the “lure of universality” and points to a “clash of two cultures”. Erikson (2013: 219) writes that the field “often mixes two distinct theoretical frameworks, creating a logically inconsistent foundation.” Hidalgo (2016) wonders whether the field is “disconnected, fragmented, or united,” arguing that social and natural scientists do not understand each other because they have different goals. However, although there is consensus on the presence of tensions between disciplines, these authors disagree about which disciplines are clashing, and why.
I argue that the hypothesis of a disciplinary divide is not sufficient, as it fails to explain why the controversy reignites in 2018—which network scientists see as “surprising” (Holme, 2019). Before we get to that point, I must briefly present NS and several concepts necessary for understanding its contentious points.
The key concepts of network science
NS focuses on the study of complex networks. Euler’s work in the 18th century gives birth to graph theory, and Moreno’s (1934)
Three types of networks, about 1000 nodes each. The complex network (center) is sometimes presented as an intermediary between order (left, a square lattice) and disorder (right, a random network).
The NS controversy is specifically about
I refer to this as the
Many researchers challenge the pervasiveness of the power law based on its resemblance to the
Mapping the controversy
The controversy unfolds in two distinct moments, characterized by the accumulation of traces in the digital public space as network scientists debate on their blogs, Twitter, and arXiv, a platform hosting non-peer-reviewed pre-prints. The first dispute happens in 2005 and focuses on the resemblance between the log-normal and power-law distributions. The second happens in 2018 and challenges more directly the measure of scale-freeness.
My methodology is based on document analysis and draws on controversy mapping (Venturini, 2010). I “follow the actors” (Latour, 1987) to identify the points they see as controversial. I often refer to the researchers involved in the debates as
The controversy has no clear boundaries. The NS concepts and methods are challenged and discussed over its two decades of existence, as for any scientific field. In this article, I specifically investigate the contentious points whose resolution is contested by actors: when they also disagree about their disagreement.
I coded a selection of 40 academic and non-academic publications related to the controversy. I explored the literature with snowballing sampling before reducing the corpus to a set of key documents. I selected explicit refutations, refuted articles, commentary, major publications citing the disputes (e.g., attempts at concluding them), and major references. See Table 1 for the list and Figure 3 for a contextualized visualization.
Corpus of documents coded for this study, chronological order.
Lines in italic indicate views expressed by actors other than the authors of the document (quotes). Data available as supplemental material.
Figures 2 and 3 help familiarize readers with the corpus. For the sake of clarity, I classified the documents into four groups. The initial references in 1999–2000 show early signs of the controversy. I gathered publications explicitly referring to each academic feud in the 2005 dispute and the 2018 dispute. The ongoing discussion group contains contributions that do not refer explicitly to either feud.
Network of citations between coded publications over time. The node size indicates the number of times cited in the corpus.
The evolution of citations (Figure 2) shows that the 2005 controversy is rarely cited by subsequent publications. The 2018 controversy largely builds on the 2007–2016 academic discussion.
Placing the documents and their type in chronological order (Figure 3) shows that two waves of reactions happen after the publication of a polemic piece: self-published web commentary in the following weeks and then, academic articles featuring refutations in the following years.
Corpus of 40 documents coded for this study, in chronological order. It includes type of document, direct and indirect refutations, and mentions of other documents in the corpus.
I reduced my qualitative exploration of this corpus to a coding of 12 different arguments framing the controversy, expressing a specific perspective on scale-freeness and universality, or taking an epistemic posture. Each of the 120 data points consists of a brief quote exemplifying a given argument featured in a given publication. The data is available as supplemental material.
I further reduced this corpus by focusing on the 13 most recurrent actors: Alderson, Doyle, and Willinger (who always published together in this corpus), Amaral and Malmgren (idem), Barabási, Barzel, Clauset, Holme, Mitzenmacher, Shalizi, Vespignani, and Watts. Figure 4 shows the co-publication groups in the corpus. These 13 key actors effectively form 10 groups or single actors. I picked this number to ensure that each presented enough material for the analysis.
Authors and their publications in the corpus. Note: it does not include authors quoted in a publication.
I compiled the statements of the key actors by period in a table available as supplemental material. It comprises 79 quotes. Table 2 presents each argument with two examples of quotes. Figure 5 features which key actor states which argument during which period.
Arguments coded in the corpus, with two example quotes for each.
Statements by key actors per period: before and during the 2005 controversy, between the two controversies, and during the 2018 controversy. Corresponding quotes are available as supplemental material.
Actors’ view of the controversy
Before engaging with the matter of the two disputes, I summarize how the actors of the controversy frame it themselves. Their recurrent arguments are the following:
A disciplinary divide A matter of how public relations are enacted by certain researchers An issue of conceptual ambiguity
Argument 1
“For Vespignani, the debate illustrates a gulf between the mindsets of physicists and statisticians” (Klarreich, 2018). A similar opinion is voiced by half of the key actors (see Figure 4), although the problem is rarely situated precisely. Holme (2018b) characterizes the divide as “emergentists” who “didn’t lose faith in the buzzwords of the nineties’ complexity science” such as “universality” versus “statisticalists” for whom “scale-freeness is not scientifically important if it is not testable.” Keller (2007) similarly points at the goal of seeking laws of nature: “biologists have been little concerned about whether their findings might achieve the status of a law. … Physical scientists, however, come from a different tradition—one in which the search for universal laws has taken high priority.” However, in contrast to the hypothesis of a disciplinary divide, Clauset insists instead on the “importance of … good statistics” regardless of the discipline (Keller, 2005).
Argument 2
Barabási’s critiques condemn his “grand claims of universality” and his “apparent arrogance” (Clauset, 2005b). The former symmetrically suggests that the latter exaggerate their claims “to get maximal attention” (Barabási, 2018). Barabási’s fiercest opponents see a scientific issue in his promotion of what they consider disproved claims: “Garbage In, Gospel Out” (Willinger et al., 2009: 598). However, Barabási always responds to the refutation of his articles (see the red arrows in Figure 3) and is supported by respected researchers (Holme, 2019). There is no consensus on the disproval of Barabási’s claims, and some even find that “all his talk about networks is good for computer science in general” (Venkatasubramanian, 2005).
Argument 3
In 2018, Clauset and Holme mention conceptual ambiguity as a cause of the controversy. More generally, many authors acknowledge the absence of a clear definition for important concepts, occasionally explained by the lack of maturity of NS as a field (Vespignani in Klarreich, 2018).
The idea of a disciplinary divide is popular after the first dispute (Keller, 2007). It may explain why the academic activity between 2007 and 2016 aims at filling a knowledge gap (most notably in Barrat et al., 2008; Clauset et al., 2009; Perc, 2014; Stumpf and Porter, 2012). The same actors were surprised when the controversy reignited in 2018, which suggests that they believed they had ended it. Klarreich (2018) quotes Vespignani: “the important question is not whether a network is precisely scale-free but whether it has a heavy tail … I thought the community was agreeing on that.” Similarly, Holme (2019) states: “I, and (I believe) most colleagues, were following the principle that ‘knowledge of whether or not a distribution is heavy-tailed is far more important than whether it can be fit using a power law’ … Thus, it was surprising that the scale-free debate would flare up again.”
First dispute: Power-law and log-normal distributions, 2005
The dispute is about the claim that observed power laws are log-normal distributions. Some argue a flaw exists in the statistical procedure used to identify power laws, thus challenging their pervasiveness. The dispute unfolds as follows.
In May 2005, Barabási (2005) publishes an article on the presence of “heavy tails in human dynamics”.
In October, Stouffer et al. (2005: 1) publish on the online repository arXiv 1 (no peer review) a refutation of Barabási’s claim that “the dynamics of a number of human activities are scale-free.” They argue that “the reported power-law distributions are solely an artifact of the analysis of the empirical data.”
In the days following the release of Stouffer et al.’s pre-print, other researchers comment on the dispute on their respective blogs (Clauset, 2005a; Shalizi, 2005; Venkatasubramanian, 2005). Clauset (2005a) frames it as a matter of “good empirical research” and summarizes the main sticking point as such: “[Stouffer et al.] eliminate the power law as a model, and instead show that the distributions are better described by a log-normal distribution.”
Venkatasubramanian includes Mitzenmacher in the controversy. Venkatasubramanian interviews Mitzenmacher, defending the impossibility of contrasting the two distributions in practice, as he had established in a previous publication (Mitzenmacher, 2004).
In November, Barabási et al. (2005: 2) publish a response to Stouffer et al.’s rebuttal, on arXiv as well. First, they acknowledge that both distributions match observations, but add that Stouffer et al.’s claim stems from a misunderstanding of the original data set. Second, they argue that their work “fails to propose an alternative mechanism indicating that a lognormal distribution could also emerge,” and therefore, “is a mere exercise in statistics, one that has little hope to be conclusive” on a larger data set. From that point in time, Mitzenmacher’s argument on the relative irrelevance to contrast the log-normal and power-law distributions meets consensus in the community.
In a second blog post, Clauset (2005b) comments on the dispute, and like Mitzenmacher, reframes it to account for the role of Barabási’s rhetoric in the reception of his work: Barabasi is not one to shy away from grand claims of universality.
Between the two disputes
After a second pre-print from Stouffer et al. (2006) refining their argument, the dispute moves to the classic academic space of peer-reviewed publications. At this point, most authors acknowledge that “whether or not a distribution is heavy-tailed is far more important than whether it can be fit using a power law” (Holme, 2019).
A series of publications contest specific claims on scale-freeness. Keller (2005, 2007) refines her epistemic critique of universality. Malmgren et al. (2008, 2009) show that heavy-tailed distributions in complex networks are not necessarily caused by preferential attachment and propose an alternative model. Muchnik et al. (2013) support the point. Alderson et al. (2019) keep refuting the scale-free model in the case of internet, a critique they formulate during every phase of the controversy, but without mentioning either dispute (Doyle et al., 2005; Willinger et al., 2004, 2009).
Clauset solidifies his position with the help of Shalizi and Newman (Clauset et al., 2009). They develop a rigorous framework for testing scale-freeness, confirming certain empirical observations of power laws and ruling out others.
Stumpf and Porter (2012) also publish an article presented in 2018 as the final point on the controversy. 2 “The most productive use of power laws in the real world will … come from recognizing their ubiquity … rather than from imbuing them with a vague and mistakenly mystical sense of universality” (666).
Despite critiques, Barabási keeps supporting the argument of universality, albeit under a weaker form (Barzel and Barabási, 2013). The situation leads Pachter (2014) to comment on his blog that “Barabási’s ‘work’ is a regular feature in the journals Nature and Science despite the fact that many eminent scientists keep demonstrating that the network emperor has no clothes,” echoing the recurrent claim that the pervasiveness of power laws is a “myth” (Lima-Mendez and Van Helden, 2009; Shalizi, 2010; Willinger et al., 2009).
Barabási publishes the book
The second dispute makes visible why the disagreement persists. Before I get to this point, I must establish how the controversy differs from its depiction by actors, so that we can see beyond the hypothesis of a disciplinary divide.
The actors’ positions during the first dispute
I account for the position of key actors on scale-freeness across the two disputes by tracking the four following statements, systematically coded for the 40 publications of the corpus:
We CAN contrast the power-law and log-normal distribution in empirical situations. We CANNOT contrast them. Scale-freeness requires a better statistical characterization. A basic test of scale-freeness is useful to science even if it is not perfectly rigorous.
I use these statements as an analytical grid of argumentative positions that key actors may or may not occupy during each dispute. I show this grid visually for ease of understanding. As only the first two statements are mutually exclusive, I juxtapose only them. According to the key actors’ narrative, “statisticians” defend the possibility to contrast distributions, and “physicists” argue that it does not matter in empirical situations. I position the statements accordingly, as illustrated in Figure 6.
Positions in the narrative of a disciplinary divide. Dashed boxes represent the positions contingent to each side.
How the first dispute unfolds,
How the controversy was supposed to close,
Why the controversy reignites in 2018 despite this considerable reconciliation effort is worth investigating. I visualize the coding of key actors (Figure 5) using this grid in Figure 9, for convenience. Notice Clauset’s trajectory, as he follows the sequence in reverse: He starts in the “happily ever after” position (Figure 8(b)) in 2005 and moves to the typical “statistician” position (Figure 6(a)) in 2018. The second dispute is triggered by a pre-print by Broido and Clauset (2018).
Statements of key actors during three different periods. Some annotation highlights the difference with the precedent period.
Clauset actively contributes to reaching consensus until the second dispute. He refrains from framing the debate as a disciplinary matter and co-publishes with statisticians and physicists. His publications are respected and show an in-depth understanding of Barabási’s position. “Power-law Distributions in Empirical Data” (Clauset et al., 2009) is the second most-cited publication of the corpus, cited by Barabási (2016, 2018) twice. However, Clauset (2005b) also requires “falsifiable hypotheses”. It is this imperative of falsifiability, and not a disciplinary divide, that grounds his reopening of the controversy.
To understand how a criterion as consensual as falsifiability can become controversial, I need to introduce two approaches to knowledge that renders visible the epistemological commitment of network scientists, notably during the second dispute.
The nomothetic and idiographic subcultures of network science
The type of knowledge Barabási produces determines his position in the controversy. His approach postulates the existence of universal structures: Phenomena obey laws, and the purpose of science is to find them. This position is what the philosopher Windelband introduced as the Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge - nature’s
Galison (1999) remarks that “[e]ach subculture has its own rhythms of change, each has its own standards of demonstration, and each is embedded differently in the wider culture of institutions, practices, inventions, and ideas” (143). He observes how “theorists trade experimental predictions for experimentalists' results” (146). In the second dispute, I find similar interactions between nomothetic theorists, such as Barabási, and the idiographic practice of instrumentalists, such as Clauset.
Second dispute: Characterizing scale-freeness, 2018
The second dispute focuses directly on scale-freeness. It extends the first one, with similar arguments and involves some of the same actors, but unfolds differently.
In 1999, Barabási and Albert publish two famous articles. In the first one (Albert et al., 1999), they study the structure of the World Wide Web and measure that the probabilities of a page to cite or to be cited “follow a power-law over several orders of magnitude” (130). In the second (Barabási and Albert, 1999), they introduce the concept of preferential attachment and measure multiple data sets to conclude that “large networks self-organize into a scale-free state” (510). This article, considered a pillar of network science, states for the first time the disputed point: that scale-freeness is pervasive.
In January 2018, Broido and Clauset publish on Across scientific domains and different types of networks, it is common to encounter the claim that most or all real-world networks are scale free. The precise details of this claim vary across the literature … Some versions of this “scale-free hypothesis” make the requirements stronger … Other versions make them weaker. (1)
In the following days, Holme (2018a) comments in a blog post that “if we could rewrite history and redefine power-laws as ‘something that follows a straight line in a log-log histogram if you squint from the side of a computer screen’, then they would, for sure, be abundant” (the reconciliation position, see Figure 8(b)).
In the following days, Barzel (2018) publishes a short piece online aligned with Holme’s position: “the meaningfulness of scale-free supersedes its detailed empirical accurateness.” He finds the discussion “roughly aligned along a disciplinary divide”.
One month after Broido and Clauset’s pre-print, Klarreich (2018) publishes a piece in
Two months after the publication of the pre-print, Barabási (2018) issues a rebuttal on his website. This self-published piece is more didactic and more polemic than a typical academic publication. For him, Broido and Clauset fail to recognize the scale-free mechanism “[b]y insisting to fit a pure power law to every network, and ignoring what the theory predicts for any of them.” Barabási also challenges the relevance of their procedure: “And the real surprise? Even the exact model of scale-free networks, following a pure power law, fails their test. … The true failure is their methodology: It fails to detect that the gold standard is scale-free.” He concludes that “the study is oblivious to 18 years of knowledge accumulated in network science.” His response ignores the question of falsifiability, and challenges the relevance of the measurement procedure.
In November, Holme (2018b) exposes “the state of affairs” in another blog post: “Simply speaking, there are two camps: those seeing scale-freeness as an emergent property, and those seeing it as a statistical property.” On one side, “emergentists … view scale-free networks essentially as outlined in Barabási and Albert’s Emergence of scaling in random networks, … [and] didn’t lose faith in the buzzwords of the nineties’ complexity science: universality, fractals, self-similarity, criticality, emergence.” On the other, “statisticalists [argue] that scale-freeness is not scientifically important if it is not testable … [and] are on top of the latest data science trends.” He concludes that “[t]he disappointing realization is that whether scale-free networks are rare [or not] is really a choice that needs to be argued by words”—a nice example of Kuhn’s (1962) “paradigm incommensurability”.
On 4 March 2019,
Broido and Clauset’s (2019) revised article is substantially the same, retaining the original data and analysis, making the argument clearer and more solid. They clarify that their definition of scale-freeness is not based on preferential attachment and add a “robustness analysis” section implicitly addressing Barabási’s technical and conceptual concerns.
Holme (2019) summarizes the controversy and reflects on it. For him, the “controversial topic” is to know whether “scale-free networks rare or universal” and “important or not”. He argues that “in the Platonic realm of simple mechanistic models, … the concepts of emergence, universality and scale-freeness are well-defined and clear. However, in the real world, … they become blurry. … Now we have one camp … thinking of scale-free networks as ideal objects …, and another seeing them as concrete objects belonging to the real world.” He suggests finding consensus by acknowledging the legitimacy of studying complexity-related notions, such as scale-freeness, and the need to build a better statistical framework. He remarks finally that “it often feels like the topic of scale-free networks transcends science.”
The unresolved tension between idiographic and nomothetic subcultures
The argument of universality is divisive. My coding identified six publications stating it (four co-signed by Barabási), and nine publications criticizing it. Only one does both (Barrat et al., 2008), making a similar point as Holme: Universality is a defined concept “related to the identification of general classes of complex networks” (76), but “all knowledgeable physicists would agree” that “the quest for universal laws … cannot apply to network science” (296). The other publications mentioning universality pick a side.
Although a formal critique of universality for complex networks exists since at least 2005 (Keller), Barzel and Barabási (2013) disregard it. They acknowledge that “a mathematical framework that uncovers the universal properties of [complex networks] continues to elude us” (673) but do not question the idea itself.
Keller develops the most precise argument against universality. She identifies a “clash of two cultures” with the “tradition … in which the search for universal laws has taken high priority,” i.e., the nomothetic approach (2007). For her, the argument of universality is invalid, and successful only for reasons external to the criteria for scientific truth. She explains the “faith in … ‘the unique and deep meaning of power laws’” by “the rapid growth of the sector of the publishing industry” and “the remarkably effective uses of language employed in presenting these ideas” (2005: 1067). However, as power laws “are not as ubiquitous as was thought,” and it “tells us nothing about the mechanisms that give rise to them,” the claim “that scale-free networks are a ‘universal architecture’ … are problematic” (2007).
The “clash” is not about the universality of scale-freeness; this is just a disagreement. The clash is about the
Clauset and Watts focus on falsifiability, in the classic Popperian sense. It shows that they see universality as a hypothesis, an evaluable statement. Clauset remarks early that Barabási’s work does not “provide falsifiable hypotheses” and later, that the “scale-free hypothesis” (Broido and Clauset, 2018) “sounds like a nonfalsifiable hypothesis” (Klarreich, 2018). Watts criticizes that “the claim just sort of slowly morphs to conform to all the evidence, while still maintaining its brand label surprise factor” (Klarreich, 2018).
In contrast, Barzel and Barabási’s (2013) nomothetic approach proceeds by postulating universality, for instance, when they seek “a mathematical framework that uncovers the universal properties of [complex networks]”. Barabási’s position on modeling also shows this. I coded the argument that
The different sides of the dispute implicitly disagree on the validity conditions applicable to universality. For Clauset and Watts, universality is a hypothesis that can be proven or disproven. For Barzel and Barabási, it is an epistemic device.
The
Conversely, Keller does not acknowledge universality as a constituent of the nomothetic epistemology. She presents the physicist’s “traditional holy grail of universal ‘laws’” (2007) as if it were a horizon, while it is, instead, part of their way. Asking Barabási to abandon his “faith in, as he says, ‘the unique and deep meaning of power laws’” (2005: 1066) can be only as successful as asking a physicist to reprove physics.
Keller’s position is
Contrary to Keller, Clauset seems to fully understand the nomothetic approach, and to acknowledge it. As we have seen, he defends Barabási’s early “apparent arrogance” and legitimacy to publish a finding “that is merely suggestive so long as it is honestly made, diligently investigated and embodies a compelling and plausible story.” However, Clauset (2005b) also demands “falsifiable hypotheses by which [Barabási’s claims] could be invalidated.” His refutation in 2018 does not touch upon the postulate of universality, but its empirical validity conditions.
The nomothetic quest for universal laws requires by nature changing theory in the face of evidence: The better model replaces the worse. Evidence always has some degree of looseness in this context, as laws are only as good as the experiments. Barabási opposes this argument to Clauset, insisting that his “findings do not undermine the idea that scale-freeness underlies many or most complex networks” (Klarreich, 2018). But “Clauset doesn’t find this analogy convincing” and replies that “it is reasonable to believe a fundamental phenomenon would require less customized detective work” (Klarreich, 2018). Clauset et al. (2009) defend a decade-old agenda of assessing the experimental validity of scale-freeness.
Barabási’s experimental program is derived from theory (it is, nevertheless, empirical). His pioneering work on scale-freeness (Barabási and Albert, 1999) prompted multiple authors to seek it in various contexts. The subsequent wave of empirical findings reinforced his claim for the pervasiveness of complex networks (list in e.g. Lima-Mendez and Van Helden, 2009). As Galison (1999) observed in another context, theorists (Barabási) “trade experimental predictions” (pervasiveness) “for experimentalists’ results” (146).
The experimental program gradually affirmed by Clauset is that of an experimentalist. It leaves behind the model-based goals of theorists and focuses instead on experimental validity—Popperian falsifiability. By reclaiming the right to invalidate theory by experiment, Clauset challenged Barabási’s nomothetic program and set foot on idiographic ground.
Galison (1999: 146) makes relevant remarks on the situation: the two subcultures may altogether disagree about the implications of the information exchanged or its epistemic status. For example, … theorists may predict the existence of an entity with profound conviction because it is inextricably tied to central tenets of their practice … The experimentalist may receive the prediction as something quite different, perhaps as no more than another curious hypothesis to try out on the next run of the data-analysis program. But despite these sharp differences, it is striking that there is a context within which there is a great deal of consensus. In this trading zone, phenomena are discussed by both sides. … It is the existence of such trading zones, and the highly constrained negotiations that proceed within them, that bind the otherwise disparate subcultures together.
Barzel (2018), Vespignani, Watts (Klarreich, 2018), and Holme (2019) acknowledge the importance of Broido and Clauset’s (2018, 2019) work. Of course, it promises better validity standards for the field. But more importantly, by declaring a new experimental program, their work shows the way out of the long-lasting controversy.
I suggest a plausible interpretation of the controversy. The accumulation of evidence against the universality of scale-freeness weakened Barabási’s empirical program. However, most actors still agree on the pervasiveness of complex networks—whatever that means. As Broido and Clauset’s program is resilient to the critique of universality, actors may adopt it to design their own experiments. I see theorists and experimentalists as the two legs of the field. When the theoretical leg weakened, the weight naturally shifted to the experimental leg. The controversy made visible an otherwise latent difference of perspective.
Conclusion
In this article, I account for a long-lasting controversy in network science on the nature of scale-freeness. The first dispute in 2005 focuses on the similarity of the power-law and log-normal distributions; the second, in 2018, on the statistical characterization of scale-freeness. Many network scientists have commented on the situation, generally framing it as a conflict between physicists and statisticians, and assuming that the controversy had been settled around 2010. Thus, they were surprised by its resurgence.
I propose another interpretation that better accounts for the resilience of the controversy. The core disagreement lies in the epistemic status of scale-freeness: a sign of a universal law for some, characterization of empirical phenomena for others. Like Galison (1999), I observe epistemic subcultures with different approaches to knowledge. Theorists elaborate models and predictions. Experimentalists stabilize the procedures necessary to account for empirical phenomena. These subcultures do not have the same epistemic perspectives, or the same goals.
We can describe these stances with what the philosopher Windelband introduced as
I argue that the controversy was caused by the rise of an experimental program challenging the theory-driven approach dominant in the field. Theorists (e.g., Barabási) insist that experiments on scale-freeness draw their validity only from a model. Experimentalists (e.g., Clauset) defend the measurement of scale-freeness with model-independent methods. This disagreement on the epistemic status of scale-freeness existed before the dispute, but became visible as each party argued for their own program. The recent endorsement of Clauset’s endeavor by theorists (e.g., Holme) suggests a shift in the field in favor of the experimentalist perspective.
The dynamic of network science offers several lessons in the era of digitization of the social sciences and humanities. Commonplace is the defiance of some scholars regarding the methodological imperialism of natural sciences, or what they perceive as such. The critique has merit, but it might be misplaced in the case of network science, as epistemic gaps do not run along disciplinary lines. Nomothetic positions in the social sciences cause trouble, but powerful idiographic positions also exist within the natural sciences. When something like the network circulates inside science, it moves with an assemblage of theories, experimental results, and material-semiotic practices, including tools. This assemblage is equivocal by nature, and can be received in different ways. Freeman (2008) documented how network centrality circulated from social network analysis to network science and to physics, supporting idiographic practices in physics as it supports nomothetic practices in sociology.
Transdisciplinary fields like digital methods and computational social science are natural zones of dialogue where network practices and predictive models trade knowledge despite their different epistemic perspectives. As this hybridity is sometimes misconstrued as a threat to idiographic practices, I find it useful to remind that idiographic practices exist in the natural sciences, that influence can go both ways, and that we can collaborate without abdicating our respective approaches to knowledge—whatever they are.
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