Abstract
Progress in theorizing networks and events requires formulating a greater diversity of networks and, in particular, enabling network analysis to exploit relations between events and the attributes, actions, and variables that characterize them. We advance this line of inquiry in dialogue with a recent approach to the systematic study of violent conflicts among state actors and groups of people who refuse to accept their governments’ power. One productive way to analyze an insurgency is to view it as a network of sequenced events across stages (periods) of conflict. We explore this formulation, identify limitations, and present illustrative analysis demonstrating how new and useful insights can be obtained by combining our formal approach with one grounded in the comparative analysis of case studies.
Reconciling Variable-Centered and Relational Inquiry
Sharp distinctions are often drawn between relational and variable-centered modes of sociological inquiry and (for the most part) rightly so. Classically, each variable or attribute of a social actor (e.g., education or income) was postulated to have a singular causal meaning not dependent on past sequences of attributes or variations among the institutions or the social networks within which actors are situated. This led prominent theorists to call for rejection of construal of the social world as a “general liner reality” (Abbott 1988:181). Variable analysis tends to detach elements from their spatiotemporal contexts and is an example of “substantialist thinking” placed in opposition to the “relational” perspective (Emirbayer 1997:288).
Notwithstanding this dominant view that draws a sharp demarcation between variable-centered and relational research and theorizing, there have long been efforts to theorize relational approaches that can effectively exploit multivariate data contexts. Early on, Sorokin (1927) envisioned social mobility as family and individual trajectories through a multidimensional space of variables. In Sorokin’s work, the structural duality of persons and groups—“The biography of a man in its essence is largely a description of the groups to which the man has had a relation, and the man’s place within each of them” (p. 6)—was broadened to a framework within which variables provided a multidimensional space of network relations among categories, such as “Protestant” and “engineer,” based on the relative intensities of intermarriage or mobility of people among the categories. Later on, social-relational or “associational contiguity” of occupations was depicted by multidimensional diagrams of mobility or friendship relations among macro occupational categories and socioeconomic status (on the scale of a metropolis or an entire nation), thus harnessing variables to depict relations (Blau and Duncan 1967; Laumann and Guttman 1966).
There was a time when network analysis was concerned exclusively with who-to-whom (“one-mode”) data. Much of the history of network research, however, has been written as the result of an expanded vision as to what constitutes a network. Consider for example: affiliation (or who-to-what) networks (Fararo and Doreian 1984); multimode, multilevel, and multiple network formulations (Lazega and Snijders 2016); and McPherson’s ecology of organization types, with types situated as possibly overlapping regions within a property space defined by sociodemographic variables (McPherson 2004), recently incorporated within a theory of dual alignment networks (Puetz 2017). Pioneers such as Burt (1981:316) began to envision connections between the usual concept of an actor’s network position (as embedded within webs of social relations) and “combinations of attributes defining statuses in . . . social structure,” the result being that survey data on samples of respondents could be used to study relational patterning, as in Burt’s (1991) use of survey data on social relations to construct a network among categories of the variable, years of age. Recently Breiger and colleagues (Breiger 2009; Breiger and Melamed 2014; Melamed, Breiger and Schoon 2013) have demonstrated that the usual techniques for linear modeling of variables in a standard cases-by-variables data format, including multiple regression and many of its generalizations, have a “dual” formulation as networks among the cases, thus leading these researchers to develop specific models of “the duality of cases and variables” that are widely applicable to the general linear model as well as to Charles Ragin’s qualitative comparative analysis.
The review just concluded is our brief in favor of theorizing networks of relations among (individual or collective) actors on the basis of the attributes or variables they have in common and, dually, taking variables or attributes or even (as we shall see) actions as the nodes and examining relations among them. This motivation, while (as we have tried to suggest by our review) it is trending in social network studies, is not yet widely accepted, due to the emphasis of many network analysts on studying relationships among tangible actors, individual or collective, that are capable of agency (Lazega and Snijders 2016). We discuss some of the tradeoffs in our essay’s “Conclusion.”
Events
A discussion similar to the preceding informs Abell’s (2004) exploration of his formal approach to narrative analysis as an alternative to variable-centered approaches. 1 Abell conceives narratives as directed graphs (i.e., networks with no reciprocated links) in which nodes are states of the world and arcs depict “actions” that connect earlier to later states. Abell refers to pairs of connected states as “events.” The crucial analytic procedures of interest to Abell pertain to the comparative study of narratives, which allows pursuit of the question as to “what the social mechanisms are which generate [the] patterns of covariation” among them.
We propose a formulation of networks of events that is influenced by Abell’s focus on comparative analysis of directed graphs but differs from his approach in many ways. This is because we are concerned with states of the world, each of which may be characterized by (often many simultaneous) attributes, variables, and actions. For us, earlier attributes, variables, and actions are connected to later ones within a directed graph by arcs that depict temporal precedence: Variables from an earlier period may persist or change in the next subsequent period. Comparative analysis consists in comparing the patterning of changes in states across multiple directed graphs, each of which represents a case of the phenomenon of interest.
Insurgencies
Our departures from Abell’s approach result from the specifics of our data context. As was also true of Schoon’s (2014) innovative study, our data set pertains to the world’s 30 most recently begun insurgencies that terminated in the interval from 1978 to 2008 (Paul, Clarke, and Grill 2010a; Paul et al. 2013). 2 In-depth qualitative analyses, confined however to available English-language sources, were constructed and published in a 327-page volume (Paul et al. 2010b). In addition to the case studies, an extensive list of variables was constructed; each variable was measured across all the cases. 3
Because insurgencies are not homogeneous across time, the researchers divided each case into two to five phases, not of uniform duration. “A new phase was declared when the case analyst recognized a significant shift in the COIN [counterinsurgency] approach, in the approach of the insurgents, or in the exogenous conditions of the case” (Paul et al. 2010a:7). Phases were not intended to capture micro-changes or tiny cycles of adaptation and counter-adaptation; rather, the authors understood their within-case chronological partitioning as macro-level or “sea-change” phases. In this paper, we are concerned with 75 variables for each of the 86 (in total) phases of the 30 cases. The cases studies, all the coded data, and a great deal of analysis by the original researchers are publicly available. 4
Insurgencies as Networks of Event Orderings
We need to call the reader’s attention to the nature of the 75 “variables” because these codings are highly distinctive in the study of Paul et al. (2010b). To begin by quoting some examples (where COIN is an abbreviation for governmental, counter-insurgent forces):
Variable 4 [V4]: “COIN forces established and then expanded secure areas.”
[V2]: “In area of conflict, [the] COIN force [was] perceived as not worse than insurgents.”
[V38]: “Majority of population in area of conflict supported/favored COIN forces (wanted them to win).”
These are certainly not “variables” in the ordinary sense of that word. They strike us more as researchers’ claims about actions or activities. Each of the 75 variables is coded (as present or absent) in each of the 86 (total) phases of the 30 cases (they are situated as to time and place).
We began our research highly puzzled about the meanings of the variables and their relations to one another. What, for example, is the difference (if any) between [V2] and [V38]? Does expanding secure areas [V4] lead to more favorable perceptions [V2], or does it work the other way around? Or perhaps these variables accompany each other? And how do the relations among the variables differ by types of case (Breiger 2009)? These are examples of questions at the heart of how insurgencies unfold.
Cross-case Interpretation of Intersecting Orders of Events
We constructed, for each case, a network among the variables defined by chronological precedence. If some variable, say [V
i
], appears in phase
An example appears as Figure 1 (ignoring differences in line shading, which will be explained presently), which shows the precedence relations among the 75 variables for the case of the Afghan Taliban in the period 1996 to 2001. Technically, Figure 1 reports a Hasse diagram of a partial order (Birkhoff 1948). Variables that have identical antecedents and also identical subsequent relations are grouped together equivalently at the same level in the Hasse diagram (thus: [V2] = [V4] = . . . = [V75] in Figure 1). And crucially, such a diagram does not include transitively implied relations (see also Martin 2009:174–75). For example, we can infer from Figure 1 that [V3] precedes [V68], even though that arc is not shown in the diagram, because the diagram reports that [V3] precedes [V34] (for example) and also shows that [V34] precedes [V68]. We will interpret Figure 1 after introducing our technique for comparing event orderings across multiple cases of insurgency.
Precedence relations among variables (Hasse diagram) for two cases.
Since each case of insurgency is depicted as a Hasse diagram, we compute the intersection of multiple cases as the Hasse diagram of the intersection of their respective inclusion orderings. An example—the Hasse diagram of the intersection of the Afghan Taliban insurgency in the 1996–2001 period (introduced previously) and that in the Democratic Republic of Congo (DRC, 1998–2003)—is shown in Figure 1 as the subset of precedence relations (depicted as heavy arrows) connecting the subset of variables (shown as rectangles with beveled borders) that are present in both cases. The Afghan case (1996–2001) extends in time from the Taliban seizing power from an unstable mujahadeen government until the external intervention of a U.S.-led coalition (on the side of the insurgents including the Afghan Northern Alliance) drove the Taliban from power in the fall of 2001. The Congo case began with the invasion by Rwanda and Uganda in 1998 to overthrow DRC President Laurent Kabila and ended in 2003 when Kabila’s son Joseph (following the father’s assassination) eventually concluded a cease-fire with the foreign troops and entered into a power-sharing deal with the major rebel groups. The researchers coded the Afghan Taliban case as an insurgent win, and they coded the DRC case as a mixed outcome favoring the insurgents. Beyond or (said better) in conjunction with the case studies, what can intersections of 75 variables tell us about the similarities and differences among these cases?
By construction, the intersection (heavy lines and beveled boxes) in Figure 1 purports to show what these two insurgencies have in common. Thus, the beginning of the orderings in both cases is favorable to the (respective) government: The majority of the population in the area of conflict wanted the Taliban or DRC government forces (respectively) to win [V38], and the government actions did not contribute to substantial new grievances [V46]. Eventually, each insurgency featured actions of one or both sides that precipitated or constituted ethnic or religious violence [V74]: in Afghanistan, the conflict between the largely Pashtun southern regions highly sympathetic to the Taliban and opposed to the northern Tajiks and related ethnic groups; in the Congo, in addition to the regional ramifications (with Rwanda, Uganda, and Burundi allied against Angola, Zimbabwe, and Namibia, many of which were states fighting against their own rebel groups), the conflict entangled the DRC’s ethnic antagonisms between Hutus, Tutsis, and other groups (Paul et al. 2010a). Following the ethnic conflict, in both these cases, were events favorable to the (respective) insurgents: COIN forces failed to adapt to changes in tactics or operations of their adversaries [V53], insurgents de-legitimized the COIN forces [V56], external professional military forces (the U.S., in the Afghan case) fought on behalf of the insurgents [V64], and the insurgent forces were more professional than those of the government [V70]. The formal diagram of the intersection structure (heavy arrows and beveled rectangles) in Figure 1, especially with its emphasis on ethnic conflict as a funnel and the role of external professional militaries, helps us see the common features of these cases.
Comparing the two cases in Figure 1 helps researchers understand what about the Afghan Taliban case differed from the DRC insurgency. For example, the government (Taliban) forces in Afghanistan were able initially to maintain a perception of security among the population in areas they controlled [V3 and precedence relations depicted as thin lines]; this feature was not operative in the Congo. Subsequently, in Afghanistan, indigenous forces conducted a majority of the counter-insurgent operations [V45]; this was not true in the Congo case. These comparisons illustrate how the formal depictions of intersections (and conversely, gaps) in precedence relations provide additional insight in conjunction with the detailed case studies.
Quantifying a Network of Cross-case Comparisons
We can count the number of precedence relations in both event orderings (i.e., the intersection of the Afghanistan 1996–2001 and the Congo 1998–2003 cases) and the number of precedence relations in either (i.e., the union). The ratio of these counts (intersection/union) is the well-known Jaccard similarity coefficient. We can also compute the Jaccard similarity of each case with the intersection. For the Taliban case (Figure 1), the coefficient of similarity with the intersection is .42, whereas for the Congolese case, it is .34. We thus learn that the intersection is a more faithful representation of the former case than of the latter.
A network of insurgencies may be created, with relations among insurgencies measuring the degree of overlap among their sequenced activities. Jaccard coefficients among all pairs of the 30 event orderings (one for each case study) are shown in Figure 2; coefficients above an arbitrary threshold (.22) are those shown as the network ties. (The pattern is robust across a range of thresholds; results available from first-listed author.) Figure 2 also indicates the outcomes of these 30 insurgences as coded by Paul et al. (2013): government wins, insurgent wins, and mixed outcomes (all of the latter being seen by the authors as favoring the insurgents, as in the Congo case reviewed previously).
A network of similarity coefficients among 30 networks of event orderings.
There are two especially remarkable features of Figure 2. First, without exception, all cases of government wins are very close in Jaccard similarity space (at the lower right of Figure 2). The network among insurgency event orderings is informative as to sequences leading to outcomes of interest. The intersection of all eight event orderings for government-win cases is a lattice with three levels: First, government forces do not employ culturally inappropriate outsiders [V44]; next, insurgents demonstrate potency in attacks [V54]. Two paths lead forward from this node: In one, COIN forces are strong enough to force the insurgents to fight as guerillas [V69]; in the other, insurgents cause high civilian casualties or act in other inappropriate ways and become delegitimized [V59], followed by significant decrease in the flow of cross-border support [V24]. In this way, we identify the common features of these eight cases.
The second especially remarkable feature of Figure 2 is that the case of Nicaragua Contras (1981–1990; labeled NIC86) is easily identified as an anomalous case, coded as an insurgent win but in the middle of the government-win cluster. In this conflict, the U.S.-backed Contra insurgents were battling the Sandinista government. The insurgent Contras were supported by the CIA, in part by means of illegal U.S. arms sales to Iran (Paul et al. 2010a). With respect to the network of event ordering, this case is anomalous because although it has all the inclusions that are common as well to the “government-win” cases (and this is “why” it is grouped with them anomalously in Figure 2), this fact is vacuous: All the variables (except one) in this case are placed equivalently to each other in the Hasse diagram. In this Nicaragua case, the only variable that stands out from the others is “COIN unable to take advantage of air power” [V68]. On this point, we learn from the case study that despite Congressional reticence to provide more aid to the insurgents after the Iran-Contra scandal became public in November 1986, nevertheless “the Contra insurgents were able to acquire [presumably, from clandestine U.S. sources] shoulder-fired missiles, which were used to shoot down [Sandinista government] helicopters” (Paul et al. 2010a:71). In this way, our procedure leads us to identify and understand anomalous cases.
Turning to the common features of the 14 cases of insurgent win, two variables (which are equated to each other) are common to all these cases: Insurgents demonstrated potency through attacks [V54], and COIN forces employed collective punishment [V26]. This relative lack of structure suggests that it would be productive to not treat all 14 “insurgent-win” cases as homogeneous but instead to seek clusters of cases (whose intersections would exhibit richer structure) within this set of 14. However, even when all 14 cases are considered together, there is the notable common feature (as mentioned) that insurgent attack potency combined with the government engaging in collective punishment is exactly what all these “insurgent-win” cases have in common.
Conclusion
The first point to emphasize in closing this essay is that all empirical work reviewed here is meant primarily to explore and illustrate the kind of analysis that can be envisioned and carried out in data contexts like ours. We do not believe, nor should the reader, that we have at this early stage of our research a workable toolset. Many decisions we made need to be rethought as to possible alternatives: For example, we could study the presence of a variable at phase
Having established the exploratory nature of our work to date, we nonetheless have cause to continue this line of research. We have shown that one productive way to analyze an insurgency is to view it as a network of sequenced variables across stages of conflict. A network of insurgencies may be created, with relations among insurgencies measuring the degree of overlap among their sequenced activities. The network among insurgencies may be informative as to sequences predicting outcomes of interest. The sequences common to insurgencies of certain types (e.g., “government wins”) may be identified. Anomalous cases (e.g., NIC86 in Figure 2) may be identified and examined. Finally, this line of research provides an addition to the growing body of research that seeks to use network analysis to exploit relations of cases and variables.
Footnotes
Acknowledgements
We are grateful for comments and suggestions from the organizers and participants in the Networks and Events workshop at Yale University, discussions with H. Brinton Milward and Charles Ragin, and feedback from the anonymous referees. This article is based on work supported by the U.S. Department of Homeland Security Science and Technology Directorate under Grant Award Number 2012-ST-061-CS001. All views and conclusions are those of the authors alone.