The Structure of Node and Edge Generation in a Delusional Social Network*

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VOLUME 18 , ISSUE 1 (December 2017) > List of articles

The Structure of Node and Edge Generation in a Delusional Social Network*

John Levi Martin *

Citation Information : Journal of Social Structure. VOLUME 18 , ISSUE 1 , ISSN (Online) 1529-1227, DOI: 10.21307/joss-2018-005, December 2017 © 2018.

License : (CC-BY-4.0)

Published Online: 26-June-2018

ARTICLE

ABSTRACT

A rare set of data on a changing social network of personalities, drawn by a sufferer of Multiple Personality Disorder are investigated using random graph theory. The key features guiding the patient’s production of these wholly delusional networks, features which define her “schema” of social network, are derived by fitting a family of nested distributions. From this, we can derive a tentative hypothesis of how the laity may understand the logic of social networks, a hypothesis that is consonant with other forms of informal evidence.

Graphical ABSTRACT

THEORY

Schemata and Networks

We spend a great deal of time attempting to test our ideas of the structure of social networks, but very little on the structure of our ideas about networks. However, lying underneath our mathematics are root conceptions of what a social network is, conceptions that were probably first formulated in British social anthropology in the mid twentieth century (e.g., Barnes 1954), but which then quickly spread—along social networks?—to the laity. We know that many English-speakers understand the conception of a social network, and its verbified form, “to network”, but we know very little about how the laity think of social networks.

A common idea in structural psychology is that humans have certain abstract, underlying, mental constructs that are used to process sensory information, generally called schemata (in Bartlett’s [1932] and Piaget’s [1954] sense). In the language of eighteen century philosophy, these schemata are produced by the faculty of picture-organization and construction (the “imagination”) as a way of instantiating rules that connect sensory experiences to the concepts of the intellect (Kant 1950 [1787]). A common example of such a schema is our arrangement of animal species into a nested hierarchy. Piaget’s argument was that such schemata develop via a dialectic of “assimilation” of new cases to the schema, and the “accommodation” of the schema to discrepant cases. To take a classic example from developmental psychology, a child may have experience with humans and a dog, and have a schema that involves a distinction between two legged, speaking animals (humans) and four-legged, nonspeaking animals. When a neighbor’s dog is encountered, it is easily assimilated to the existing scheme, but the first cow encountered may also be thus assimilated (“dog!”), prompting the correction of the child by adults. The child has to accommodate her schema to the actual clumping of the world, now differentiating cows from dogs.

If there is such a common schema for social networks, we do not know very much about it. There have, of course, been a number of pivotal studies in which researchers ask respondents for information on their perception of a particular social structure (see, especially, Krackhardt 1987). However, there are few in which researchers attempt to understand a respondent’s own inner conceptions of network structure. Most of the few studies of network perception involve asking subjects to draw their social networks (for example, see the very interesting work of Kuhns et al. 2015). In such cases, subjects are not free to externalize their underlying archetype for what a social network should look like; they are constrained, at least in part, to reproduce their memories.

Similarly, there is no reason to be confident that an actor’s network schema has any particular relation to the “heuristics” that she might use in forming her actual ties. This slippage is familiar from social anthropology, where one finds that actors may have one way of conceiving the logic of kinship structure—for example, the people who contribute blood as opposed to the people who contribute bone (Lévi-Strauss [1949] 1969)—and very different practical principles for coordinating their marital strategies.

How, then, would we determine the nature of underlying schema? In developmental psychology, it is common to analyze failures (as in the use of “dog” for cow). A similar approach to the study of schemata—indeed, the only evidence on the matter of which I am aware—was taken by De Soto (1960). De Soto found that social structures that were symmetric and transitive were easiest for subjects to remember. This might well imply that subjects assumed that social networks tend to the form of cliques, but it must also be noted that relations that are symmetric and/or transitive require fewer chunks of information to reproduce a set of relations.

Another way of getting at schemata, other than failure, is to allow subjects to “grow” them. As Harriet Whitehead (1987) has argued in an impressive work, branches of talk therapy that involve the patient undergoing “regression” seem to elicit an exaggerated application of certain underlying schemata. It is, as Whitehead says, all assimilation and no accommodation.1 Most important for us, the productions resulting from such therapy may also be analyzed to determine their structure principles.

Networks of Multiple Personalities

One extreme form of this sort of “growing” of a schemata through therapeutic encouragement of the faculty of the imagination came in the form of what was once called “Multiple Personality Disorder” (MPD). This is a severe psychotic condition that (with very few exceptions [e.g., Prince 1917]) arises from suggestion, often aggravated by hypnosis, on the part of mental health practitioners, usually psychotherapists, who held theories that traumatic incidents early in life (generally not manifestly remembered at the start of treatment) would have led to the fracturing of the personality (also generally not manifest at the start of treatment).2 Because the psychiatric community gradually realized that the disorder was mainly iatrogenic, the diagnosis was changed to Dissociative Identity Disorder in DSM IV (Kihlstrom 2005), with treatments urged that did not incentivize the production of new personalities; the number of new cases accordingly declined to near insignificance. Thus the vast majority of cases are bracketed by the 1973 publication of the popular (and untrustworthy) Sybil that brought the condition to the public eye, on the one hand, and the 1994 DSM IV on the other.

During its heyday, many therapists who believed in MPD thought it necessary to, in therapy, explore and treat each of the personalities—no doppleganger left behind—and therefore encouraged the patient to systematize her understanding of the personalities. This also meant that patients were inadvertently rewarded for producing them, and the number of alters tended to increase with the length of the therapy. Past a certain point, it often became difficult for the patient to keep the alters apart; to make sure that they are recognizable, the alters tend to occupy extreme positions on the sorts of dimensions that twentieth-century Americans considered significant (sex, race, age, and ethnicity), using often rather crude stereotypes (Hacking 1995: 77). Presumably, in other cultures, class and/or region might be the more salient attributes, as these form the root schema for the dispersion of personhood. Thus, the patient makes use of widely shared schemata to solve prosaic problems of cognitive load. Something similar may happen regarding the form of the organization—sufferers rely on underlying general formal schemata of social organization.

As the Gestalt theorists, among others, have emphasized, there are reasons to be distrustful of any psychology, let alone a social-psychology, built on data taken exclusively from the mentally ill (which characterized the clinical approach largely associated with the French tradition). To be sure, some mental structures are unique to the mental illness, we would be seriously misled to use the resulting data to generate hypotheses hoped to apply to the mentally healthy. However, there is good reason to think that most other mental structures of the ill, even if they are highlighted by psychosis, are common ones, only emerging unchecked or out of balance.

Most notably, delusional subjects tend to use extremely prosaic, quotidian, and widely shared knowledge in support of their delusions (which is why the delusion often strikes others as so flagrant). For example, Capgras syndrome involves subjects lacking an inherent feeling of familiarity when they see close friends and relatives; this core embodied evidence is too strong to be argued against by mere logic, and so they tend to believe that their friends and relatives are imposters or robotic replicas. The delusion that one’s family and friends are robots, however, involves no changes to sufferer’s theory of robotics; hence one man with the syndrome removed his father-in-law’s head to search for the batteries, as the absence of a visible power source had baffled him (Blount 1986). Similarly, there is no reason to think that the quotidian conception of “a social network” held by a psychotic subject who multiplies her personalities is any different from those of anyone else. Thus, we may find intriguing indications of a schemata for social networks in the production of a structure of selves among sufferers of MPD.

Treatment Conventions of MPD

The reason to be concerned about this data is not that they come from someone with a mental illness, but that, by its very nature (a iatrogenic disorder), those diagnosed with MPD were set apart from other psychiatric patients predominantly by their high suggestibility and their strong interest in maintaining relations with therapists (Hacking 1995: 31). Is there reason, then, to believe that any schema produced should be attributed to the patient and not the therapist?

It is true that, first, art therapy was widely encouraged for MPD disorders, as with others supposedly suffering from repressed memory. However, if there was any implicit encouragement as to what to represent, it seems to have been scenes of victimization, or pictorial representations of strong emotions (often featuring the patient in some form surrounded by abstract shapes indicating fear or anger). While I have found one drawing of personalities being connected (Cohen and Cox 1995: 69), here they are holding hands in a realistic portrait, as opposed to the top-down vision of a social network.

Even more, it is also true that because therapists believed that treatment required naming each personality, becoming acquainted with each and all, and then integrating the set, the exploration of such terra incognito in some cases involved getting the patients to produce some visual guide to their personalities (e.g., Bryant, Kessler and Shirar 1992). For example, one therapy guide suggested that patients be asked to draw “maps” of their personalities.3 However, Fine makes it clear that she envisions the diagram involving unconnected names—if it becomes busy, it may look like a “scattergram.” Fine does, however, suggest that in some cases it may be helpful to reduce the complexity by grouping personalities into “clusters” (1993: 143). However, most importantly, the example she provides is structured more like a Linnaean taxonomy than a network or even scattergram, with personalities divided up by virtual age and personality (Fine 1993: 141). Another prominent practitioner, Frank Putnam (1989: 142), also indicates that he assumed that the most important information to be gathered on each personality was a combination of basic demographics (most importantly, sex and age), and the function played by each in the wider system—a very sociological approach (and an interest that encouraged multiples to concentrate on developing a satisfyingly diverse portfolio of personalities).4

Other prominent practitioners (e.g., Smith 2006) used the notion of a system to describe the set of personalities. However, this also does not seem to indicate that they suggested a network orientation. Indeed, some practitioners (e.g., Ross and Gahan 1988: 42), whose attempt to have patients map the system involves a spatial aspect, begin with an orientation likely to inhibit network productions: they, like others, see the map as mostly containing data on each alter, and hence taking the form more like a spreadsheet than a network. It is significant that they propose “Alters are usually represented as circles of varying sizes with relative positions and barriers between them” (emphasis added).

In sum, there is no evidence that the network construct was one that was specifically encouraged or modeled by therapists. If there were any practitioners who had a network conception of the system, I have not been able to uncover their traces. Indeed, the author of what I believe to be the most influential guide to treatment specifically urged that “The exact form of the map should be left up to the discretion of the personality system,” because “the form of the map…provides information about the personality system’s internal metaphor”; Frank reported receiving “Mercator projection maps, pie charts, architectural blueprints, organizational personnel charts, target-like arrangements of concentric circles, clock faces, lists, and some totally unclassifiable documents” (Putnam 1989: 210f) Furthermore, the neurologists who analyzed this case and reproduced the maps would likely have noted if the patient’s therapist had given specific instructions regarding the diagrams. Thus, one is on reasonably safe ground in interpreting these productions as yielding information as to the subject’s schema for constructing networks, and not that of her therapists.

CASE AND DATA

The data analyzed herein come from a patient (“Patricia”) described by David, Kemp, Smith and Fahy (1996). Patricia was a normal child, though, perhaps related to consistently high exposure to and engagement with religious doctrine, she experienced a number of relatively common psychological problems at different times (anorexia, depression), which, at one point, led to her hospitalization. Though British, as a result of her work with her husband in a religious organization, she was in the United States, and she began an intensive psychotherapy with a practitioner reached through a Christian organization. This practitioner believed that her symptoms suggested that she had experienced repressed Satanic sexual abuse from her family members, who were, or so he surmised, members of a Satanic cult, evidence for which he eventually was able to generate.

As was common at the time, the therapist believed that the expected response of a victim of such Satanic abuse would be, as a defense mechanism, to fracture her personality. And indeed, “shortly after this, she was diagnosed as suffering from MPD” (David, Kemp, Smith and Fahy 1996). When Patricia’s husband and children returned to the UK, Patricia, on the advice of her therapist, remained in the US. (Diagnoses of MPD were nearly entirely restricted to the US, and it would not be likely that Patricia’s active involvement in MPD therapy groups and counseling would have continued had she left with her family.)

I noted above that therapists believed it important for the patient to explore her full set of alters; presumably Patricia also had such encouragement, and she produced maps of the relations between her alters. Three of the most finished maps were printed in a paper analyzing the case history (David et al. 1996). It is these that form the data analyzed herein.5

Patricia drew maps in which she placed her personalities, and connected some to others by lines. Of course, we do not know the nature of what the lines represent—whether, for example, transitions would occur more easily6 between alters connected by lines, or whether there was some affinity between those connected. In many ways, this returns us to core intuitions of early network analysts: that we are interested in some sort of intertwining of lives, but we might be unable to specify a single content to the nature of the ties involved. It is only the opportunistic concentration on schoolchildren in the mid twentieth century United States that led network analysts to focus on the relatively weak and ambiguous tie of “friendship.” Patricia’s maps presumably are indicating a more fundamental connection, one perhaps as obscure as our own strong feelings.

METHODS

Characterizing the structural contours of social networks has been perhaps the central methodological preoccupation of sociologists of social networks. The panoply of techniques, including block models (White et al. 1976), triad censuses (Holland and Leinhardt 1970; Davis 1979), and exponential random graph models (Wasserman and Pattison 1996; Handcock 2003), continues to grow. One difficulty is that many methods, even descriptive ones, entail strong assumptions about the nature of the core structural principles. At the same time, the more flexible the modeling approach, the more difficulty there is in choosing between different possible models. Very frequently, we find ourselves unable to actually fit a flexible model of a network structure that has terms for the theoretically interesting effects. Indeed, investigators are often forced to use model convergence, and not theoretical or predictive adequacy, as a criterion for the structural characterizations of networks.

Here I propose a different approach, utilizing recent advances in random network generation provided by Orsini et al. (2015). Rather than make strong claims about the logic of structure (as in blockmodeling) or attempt a parametric representation, I make classes of random networks. Each class fits some of the parameters of an observed network (for example, the degree distribution), and the classes are strictly nested, so that a model that includes an additional graph parameter will reproduce the fitted network as well as, or better than, any that excludes it. The logic is akin to that underlying the U|MAN tests (Holland and Leinhardt 1976), but here I fit a set of different graph statistics. What is key is that rather than have a probabilistic generation of the graphs, which tends to take one towards parameterization (and associated identification difficulties), here the graphs are generated by random rewiring.

I go on to show that this very straightforward approach—the only complexity is in the development of a plausible algorithm to generate the graphs7—can yield insights into the structural logic of a network, without facing problems of model indeterminacy and degeneracy that other approaches may have. It is especially useful where additional parametric information (for example, node and edge characteristics) is unavailable or unimportant.

In order, the Orsini approach produces distributions of graphs that fit: (1) first, the overall number of edges; (2) then, the degree distribution; (3) then, the degree homophily; (4) then, the average local clustering; and (5) finally, the clustering by degree. Further extension to degree homophily of neighbors’ neighbors is theoretically possible, but not implemented. For ease of exposition, I delay a discussion of the particularities of this approach until the analysis of the data allows for a more concrete exposition. In all cases, I generate 30 random graphs to maximize clarity of presentation via boxplots (as opposed to having many outliers clutter the figures). I begin with an informal description of the data, and then proceed to formal analyses.

RESULTS

Descriptive Overview

Patricia’s first graph (see Figure 1) is striking in its elegance and balance. All the nodes have degree 2 or degree 3, and, with an exception—perhaps due the unique position of Patricia her “self” at the top—it consists of triads joined in a circle. Indeed, it is a near-perfect example of Watts’s (1999) connected version of a “caveman” world. It is also a fully planar graph—it can be drawn on a two-dimensional surface with no lines crossing. Indeed, it is so simple, it seems that a formal analysis is wholly unnecessary.

Figure 1

Patricia’s 1990 Network

10.21307_joss-2018-005-f001.jpg

However, it may be more difficult to come to similar conclusions based on inspection for Patricia’s network one year later, which was much larger (see Figure 2). Some things do present themselves to the eye. First, there are now two different components, neither of which has a ring structure. Second, there is more variation in the length of ties as represented. Finally, there are four forms of node differentiation: first, that between level one alters and integrated8 alters; second, that between Christian and non-Christian alters; third, that between those within the “Sphere of the Blue Flame” and those not; and fourth, numbers placed in many of the nodes. Unfortunately, the authors of the original report are unable to reproduce the logic of these distinctions. I do not consider node attributes here, as I found little evidence of structural implications of these characteristics, other than the somewhat worrisome fact (given Patricia’s religious sensibilities), that the proportion of new alters who were Christian was substantially lower than that of the nodes present in her first map.9

Figure 2

Patricia’s 1992 Network

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With closer inspection, two other things become apparent. The first is that the way that the graph increased was not, as most of us would imagine, by the agglomeration of existing ties on to the old structure. Instead, there were ruptures at a number of points. In fact, eight of the original 18 ties were severed. (The probability of a tie being severed was substantially lower for dyads in which both alters were Christian [pr = .273] than where not [pr = .714].) Most notably, large structures were inserted between previously tied nodes: thus the entire Sphere of the Blue Flame intervened between Janey and Jude, who were tied at the bottom of the previous graph. Less drastically, we find the new Allison-related cluster to intervene between Patricia and Polly, and Jethro-Panda to intervene between Jude and Dordy; further, in a number of cases, horizontal ties were eliminated between spokes of what became a larger wheel. Thus as Ju-Ju became a very central hub, the Meg-Janey tie was broken; Dordy lost a direct connection to J.C. as he(?) became a hub; Little Joey lost his tie to Emily May when she became a hub. Furthermore, one will note that the earlier alters are not sociometrically privileged: Little Joey and Dordy become extremely peripheral.

It is perhaps also interesting that there are some unnamed nodes. In some cases, these are later assigned names, but one—the hub of the wheel at the upper left—remain unnamed. It may be that Patricia considered these nodes structurally required, though not actual. Perhaps those that gained names indicate the production of a new “alter” to fit the network requirements, but this is mere speculation. The existence of alters who refuse to provide their names is not unusual among MPD sufferers.

Patricia’s third graph (Figure 3) is substantially similar to her second. The changes are that there have been a few re-arrangements in the upper middle (including the addition of some new alters), as well as the introduction of a new, smaller, component, to be placed “behind” the initial component associated with the original “Patricia” personality. There are a few other small changes, including new ties being added to previous termini, as well as Dordy’s expulsion from the Sphere of Blue Flame, which he had previously been deliberately trying to breach. (Indeed, Dordy’s whole component, led by Jude, has been disconnected from the J.C. wheel to which it was connected in the first generation.) Finally, there is, for the first time, a presumably very downtrodden isolate (“Sawdust”, associated with, but not connected to, the component behind the main plane).

Figure 3

Patricia’s 1993 Network

10.21307_joss-2018-005-f003.jpg

Most importantly, the simpler drawing conventions used in this figure highlight the core structural vision. In many ways, it seems the inverse of the first map. There, the overall logic seemed to work from the outside in—a circular structure—and had extremely high equality between nodes. Here, the logic seems to work from the inside out, as there are a few exploding “stars” of high degree giving shape to the overall structure. Yet, as I go on to show, the most important structural feature is identical across all the graphs.

The dk-Series

To use the Orsini et al. (2014) approach, one begins by the simplest distribution, sees if it can reproduce the graph statistic fit by the next simplest distribution, and if not, proceeds to this distribution, finally comparing the succession of distributions. The simplest distribution (which they denote dk0) is a widely known one, in which we consider the class of random graphs that shares the number of vertices and the number of edges with the original (a Bernoulli distribution).10 One would then check to see how well characteristics of one’s observed graph are reproduced by most of the graphs in this distribution. Because the next step in the dk series fits the degree distribution, this is of greatest interest.

Figure 4 portrays the range of statistics for a degree distribution from Patricia’s 1990 production using boxplot conventions. The observed values are superimposed as larger circles. Thus while none of Patricia’s nodes had degree 0 or 1, an improbable occurrence under Bernoulli assumptions, they had a surprising likelihood of degree 3. All this is, of course, obvious upon inspection of Figure 1. The results for the next year’s graph, however, are less obvious. Figure 5 presents these using the same conventions as in Figure 4. One sees that, except for the distribution of isolates, the graph’s degree distribution looks much more like that of a random graph.

Figure 4

Node Degree Distribution 1990

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Figure 5

Node Degree Distribution 1992

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This occurred, in part, because the new nodes added (call these “generation 2”) tended to have lower degrees than those that were present in 1990 (“generation 1”; results not shown but available from the author). Thus, what Patricia did was largely to rupture her existing network, and add nodes. However, it is not the case that these new nodes were simply “satellites” of existing “planets.” Many of the first generation nodes themselves are reduced to such a position of spokes, and some of the new hubs are second generation.

The third graph does not involve much of a change in the overall degree distribution, or, as other analyses show (available from the authors) for the other graph statistics examined. In order to save space, I forbear from presenting these results, which largely duplicate those reached via the analyses of the second graph.

Higher Order Distributions

Given that the Bernoulli graph did not reproduce the degree distribution, I move to distributions that fit this degree distribution (dk1). The question then is whether this successfully reproduces the distribution of the average degree of a node’s neighbors, when we look separately at nodes according their degree. This may be understood to indicate degree-homophily (or heterophily)—the tendency of high degree nodes to differentially associate with high (or low) degree nodes.

Does this dk1 distribution reproduce these statistics? For the 1990 graph, the answer is not quite (see Figure 6). The observed distribution is right at the 25th percentile in the constructed distributions. This indicates that degree-2 nodes tend to be connected to degree-3 nodes, and vice versa, more often than expected. However, this degree distribution is itself so constrained, that the test is difficult to carry out meaningfully. More significantly, the observed network is not contained in the constructed distribution for 1992 (or 1993) either. Figure 7 demonstrates that this is because spokes—nodes with a single edge—tend to be tied to higher degree nodes more often than one would expect by chance. This indicates a strong tendency towards a hub-spoke structure. In other words, it is not simply that there is high variance in degree, with some low degree nodes and some high—it is that the lowest degree nodes tend to be connected to very high degree nodes, and not to other low degree nodes. (This is also seen in the 1993 graph.)

Figure 6

Degree Heterophily for 1990, under dkl

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Figure 7

Degree Heterophily for 1992, under dkl

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Given that the dk1 distribution does not encompass the observed graphs, we move on to the dk2, which fits the degree distribution of neighbors’ degree exactly. Given that the next models in the dk sequence fit the tendencies to clustering, we may ask to what extent the dk2 distribution generates the average clustering observed—that is, the tendency of triangles to be completed.11 This observed statistic is .400 for the 1990 graph, and .115 for 1992. The results of the dk2 distribution average .093 for 1990 and .009, far lower than the observed.

It is unfortunate that the Orsini rewiring algorithm is unable to generate a random sample of dk3 graphs—those that fit the observed graphs tendency for pairs of connected nodes with a certain degree themselves to have a connection to nodes of a certain degree (Orsini et al 2015: 5). However, with a graph of this size is it unlikely that many graphs other than the observed exist in this family. Fortunately, there are two other families of distributions that are nested in the dk2 that fit aspects of the degree of clustering (transitive closure). We, therefore, move to the next distribution, dk2.1, which aims to fit the overall clustering exactly.12 The question then becomes whether this distribution also fits the differential pattern of clustering by degree, which is what is fit by the next, and final, distribution, dk2.5.

For 1990, it does indeed (results not shown, but available from the author), and this is not because it is impossible to find graphs in this distribution that are not homologous to that observed, but the restricted degree distribution gives little to work with. For 1992, however, it does not, and the results are extremely enlightening (see Figure 8). Patricia’s graph is still unusual in terms of its tendency for nodes with degree 2 not to have their neighbors connected; this is in contrast to nodes of somewhat larger degree. This suggests a tendency for bridges to be built that can connect one area to another. Second, the clustering tends to be disproportionately high for the lower degree nodes (except for node 2).

Figure 8

Clustering by Degree and the dk2.1 Distribution for 1992

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This tendency is extremely meaningful, as it points to a core feature of all of Patricia’s graphs—they are perfectly planar, in that every node can be placed without any two lines crossing. Interestingly, this is not because she had an aversion to crossing lines. In the 1992 graph (Figure 2), her placement of Wendy could be shifted to avoid a line crossing, but she does not do this; this position is maintained in 1993 (Figure 3). Further, when, in 1993, new nodes are added connected to Driver (within the Sphere of the Blue Flame), they are positioned in such a way so that lines cross unnecessarily.

The conclusion is that the underlying logic of her graph is fundamentally spatial, and, moreover, in a two-dimensional space. One will notice that the relative placement of nodes is largely maintained from the first to the third production, even though relations are broken and formed.13 Recall that Watts (1999) demonstrated that the key to a small world was that it was a graph that had a characteristic path length (an average shortest length between any two points) that is similar to that of a random graph, while having a clustering coefficient significantly higher than that of a random graph. Figure 9 shows the distribution of the characteristic path length (here, the mean of the shortest path between any two edges) for each of the constructed distributions; the observed value is added as the dashed line. One can see that the path length is far greater for the observed graph than any of the random graphs, even when the degree distribution of clustering is taken into account.

Figure 9

Path Length by Distribution, 1993

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Figure 10 uses the same convention to graph the extent to which the different distributions approximate the observed clustering coefficient. As this figure demonstrates, Patricia’s graph has high clustering (though, by definition, this is fit by the higher order distributions). This sort of clustering—where one’s friend’s friend is one’s friend, for example—seems to be a natural assumption to most Americans (De Soto 1960). Further, this flows naturally from a spatial representation using few dimensions.

Figure 10

Clustering by Distribution, 1993

10.21307_joss-2018-005-f010.jpg

Finally, there is one last surprising feature of Patricia’s later networks. Her first network contains what we can call a “hollow ring” of degree 10—that is, a cycle including ten nodes, no pair of which have a distance in the graph lower than that in the cycle. (In other words, there are no “short cuts” between nodes in the ring.) Yet in her second graph, the largest hollow rings are only of size four (for example, that involving Patricia, Julie, Christine and Vanessa). Figure 11 demonstrates that this becomes an extremely implausible result in the dk distribution, once we take into account the large number of nodes with degree 2. (Although Patricia’s third map has a hollow ring of degree eight, this is still quite low considering the structural features; an analysis would look just like Figure 11.) This seems to fit a world in which we never encounter the surprising situation in which our friend’s friend’s friend’s friend’s friend’s friend’s friend turns out to be our friend. Once a chain goes “away” from one in this space, one can trust that it will never come back.

Figure 11

Size of Largest Hollow Ring by Distribution, 1992

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In sum, Patricia’s world of alters may be small in absolute terms, but it is about as big as it can possibly be. Although we do not know the nature of the edges here, it is remarkable that the path length in Patricia’s network—one contained wholly within her mind—is probably substantially larger than that of the American acquaintance network!

With this interpretation, we can return to what might first appear to be a radical change in her principles of organization from the first to the second map. It is true that the degree distribution shifted dramatically (compare Figure 5 to Figure 4). However, one thing remained the same—the general spatial organization. Patricia’s delusional network shifted from a caveman world of high equality, to one in which she increasingly organized the map by certain high-degree alters (hubs). In both cases, placement came first. This offers an interesting hypothesis regarding the lay schema for the social network. I consider this in closing.

CONCLUSION

These results come from a sufferer of MPD; whether one considers this an N of 1 or an N of 107 (the number of alters in 1993) is perhaps open to dispute, but there is no doubt that one can only derive intriguing hypotheses for further study, and not to make generalizations. Still, the transition from an N of 0 to an N of 1 is perhaps the most important step one can take. It would be ideal if we could find similar data from other sufferers. Unfortunately, no data exists to determine the prevalence of this sort of structure among sufferers of dissociative identity disorder.14

Given an absence of other data, we might consider the implications of this hypothesis—that the laity has a tendency to see networks in local and spatial terms—and note whether these contradict other bits of largely anecdotal evidence that we have on the Western schema of the social network. For one, we have the reception of the small world problem. As Watts (1999) pointed out, Milgram’s (1967) results were considered quite counter-intuitive and shocking to many. Yet, the path length for American society that he determined was, first, probably too high (it requires an ad-hoc fudge for uncompleted chains and assumes all actors have knowledge of the network, which they do not). More important, such a path length is around what would be expected under our simplest null models. What is surprising, from the perspective of random graph theory, is not the path length, but the clustering.

In everyday life, however, we are not surprised that our friends know each other. In our local world, such clustering “makes sense.” We are, however, at a loss to understand the logic of the connection of one local world to another if it does not pass through us. For this reason, we are surprised to find that such local worlds are connected. In structural terms, this means that we expect few cycles of a long length that have no shortcuts.15 We see other supporting evidence of this interpretation in the fact that in online networks, the first generation of web-log broadcasters repeatedly underestimated the degree to which information being targeted to one set of acquaintances would reach unintended acquaintances (e.g., employers, grandparents, etc.), because the two sets were assumed to be wholly disjoint (see, e.g., Tian and Menchik 2016; similar offline errors of myopia arise in poor choice of gossip subjects).

Recall that Patricia’s graph has a tendency for degree two nodes’ neighbors not to have a tie. This means that they form links, like a sausage, allowing for the whole to remain largely connected. To use the terminology of Martin (2009), Patricia’s understanding of how local structures are connected is one that involves bridges—clearly identifiable edges that are not within either clique—as opposed to welds—clearly identified nodes that are in more than one clique. (For an example of bridge, see the tie between Emily May and J.C. in the upper right of Figure 2 and 3.)

Even more, Patricia’s map has a large number of what we may call “bridge keepers”—persons who are intermediaries between two cliques, but members of neither. The remarkable “Sphere of the Blue Flame” is insulated from the more profane localities by two sets of such bridge keepers, Naomi on the right and then a chain running from Miranda on the one hand to Bryony in 1992. Again, this fits a notion that some people are intermediaries, one that recurs in discussions of the small world (e.g., Kleinfeld 2002).16 While we cannot be sure that no such partition is possible in the acquaintance network, what is more interesting is that it is not mathematically necessary—the small world graphs generated by Watts (1999) have the property that every node is pretty much equally far away from every other one. Yet, this implication seems to have been difficult for most of us to accept.

In sum, the hypothesis that the root schema for a social network is a local and spatial one has plausibility. It may be that this is because this sort of structure, even though not characteristic of the weak ties of acquaintanceship, does tend to characterize stronger relationships of close friendship. However, what is key about such a schema is that it is a structure for which myopic action is wholly adequate. The further investigation of this hypothesis, then, might shed light on strategies of social action, and where they fail.

I am grateful to Pol Colomer de Simón for a discussion of his software and to James Murphy for assistance with the interface between Linux and Windows programs, and for other kindnesses besides. Two reviewers and the editor gave comments that greatly improved this paper (or so I believe). A version was presented to the Berlin Network of Network Research, and I thank the participants for their comments and suggestions.

For example, in the modern American context, such therapy led to a large number of imagined scenes that involve the patient being probed and violated while on a table, and/or confined in a very small space. This seems a remarkable invariant, given that the identity of the aggressors—whether parents, Satanists, or aliens—was more labile, depending on the theories of the therapist involved.

However, that MPD usually began in the mind of the therapist, and not that of the patient, does not mean that it is not a real—and extremely disabling—psychotic disturbance, nor that it involves dissemblance. There is evidence that different personalities do have barriers to the sharing of information, may differ spontaneously in accent, handwriting, handedness and even visual acuity (see Wegner 2002 for a balanced discussion).

“In one of the initial sessions, the MPD patient is often asked to take a large sheet of paper and to place their names on the paper ‘in a meaningful way.’ The therapist may clarify further by specifying that the names be placed in a way that would describe ‘how similar or dissimilar the personalities feel toward or about one another’” (Fine 1993: 141f).

Now Putnam (1989: 143) did suggest that he might use something like a snowball sampling procedure to uncover “hidden” alters (which he called “chaining,” asking each new alter to report other as-of-yet unknown personalities). Yet he makes it clear that he has a “family tree” vision of the structure of personalities—an original core personality at the top, and successive branches to other personalities, and sub-personalities, and so on (126).

The first author reported that no other diagrams of hers were in his possession, and that these were by far the most complete. I thank Anthony David for this kind communication. It is very difficult for researchers to access documents created by those diagnosed with MPD; not only is the temporally bound nature of the phenomenon frustrating, as IRB rules have tightened considerably since the 1980s, but the very notion of “informed consent” became implausible in the context of a large set of often mutually antagonistic personalities, the modal situation (Frank 1989: 263).

As we shall see, some of her graphs have unconnected components, which means that transitions cannot be wholly restricted to network edges.

A reviewer points out that such algorithms do not necessarily produce a uniform probability distribution of graphs (Milo et al. 2004); while there are ways of weighting the results through importance sampling (e.g., Blitzstein and Diaconis 2011), these are not used in the Orsini et al algorithm, because they cannot be implemented for some of the more restrictive models. Despite this, Orsini et al (2015: 5) report that at least in the case of power-law graphs, the resulting distributions produced were close to uniform.

Because the goal of therapy with MPD sufferers was to integrate the various personalities, labeling some alters “integrated” seems a bit of a contradiction in terms. Could she have meant structurally integrated? None of the 1990 ties were between alters later labelled as “integrated,” and only 3 ties out of 55 possible dyads between the integrated were present in 1992. Thus the “integrated” do not seem to be particularly structurally integrated.

While 78% of the first generation alters were (later) identified as Christian, only 23% of those added in the second generation were. Further, 29% of the first generation (including the original Patricia personality) were integrated; only 10% of the second generation were.

Actually, as the Orsini program does not produce dk0 results, we here use the results from a separate routine based on igraph for R.

The dk2 distribution actually fits the average local clustering, and not the average clustering. The two are quite close, and, for purposes of comparability with other work, we here present results based on the average clustering.

See note 11.

Further, note that in Figures 2 and 3 the length of ties varies and must contain information; close alters, however, are not always connected.

However, it is quite interesting that one of the few memoirs by someone (Theodocia McLean) with this condition purports to be written by “Stormy (Alter in Theodocia’s Personal Network).” Here (2009: 292) she makes reference to an upcoming work, “Stormy Journey” in which “you will meet the network of personalities that live inside her….This book is written with the help of her internal network, and the actual writer is one of the alter, [sic] named ‘Stormy’” (this work has not appeared). Note that “Stormie” is also the name of an alter in Patricia’s network. However, the details of the two’s lives are sufficiently different that we can be certain that they were two different organisms.

It is worth pointing out that this root schema may be similar for sociologists as well; when not grappling with data, they may illustrate the concept “network” using “large world” graphs (e.g., Fuhse 2016: 15) which look more like what we mean by network than the “hairball” that results from projecting a large small world onto a plane. Perhaps this feels right because our own coauthorship networks take on the character of similarly large worlds (Moody 2004).

This belief may be due to the fact that many people experience themselves as intermediaries. When I have asked college students to draw social networks of their friendship circles, somewhere around half show themselves in between two cliques. While of course it could be that they are indeed the sorts of entrepreneurs who span structural holes (Burt 1992) and therefore achieve more than others, it is more likely a result of an egocentric view in which most of us look to the left and look the right and find ourselves in the middle, paying great attention to the complexities in our own set of relationships, while simplifying others, perhaps reducing them to cliques (as in, “I was [uniquely] in between ‘the burnouts’ and ‘the brains’”).

References


  1. Barnes, J. A. 1954. “Class and Committees in a Norwegian Island Parish.” Human Relations 7: 39-58.
    [CROSSREF]
  2. Bartlett, F.C. 1932. Remembering: A Study in Experimental and Social Psychology. Cambridge University Press.
  3. Blitzstein, Joseph and Persi Diaconis. 2011. “A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees.” Internet Mathematics 6(4); http://dx.doi.org/10.1080/15427951.2010.557277.
    [CROSSREF] [URL]
  4. Blount, G. 1986. “Dangerousness of Patients with Capgras Syndrome.” Nebraska Medical Journal 71: 207.
  5. Boltanski, Luc and Laurent Thévenot. 1983. “Finding one’s way in social space: A study based on Games.” Social Science Information 4: 631-680.
    [CROSSREF]
  6. Burt, Ronald S. 1992. Structural Holes: The Social Structure of Competition. Cambridge, Mass.: Harvard University Press.
  7. Bryant, Doris, Judy Kessler and Lynda Shirar. 1992. The Family Inside: Working With the Multiple. New York: Norton.
  8. Cohen, Barry M. and Carol Thayer Cox. 1995. Telling Without Talking: Art as a Window into the World of Multiple Personality. New York: Norton.
  9. David, Anthony, Roisin Kemp, Ladé Smith and Thomas Fahy. 1996. “Split Minds: Multiple Personality and Schizophrenia.” Pp. 122-146 in Method in Madness: Case Studies in Neuropsychiatry, edited by Peter W. Halligan and John C. Marshall.
  10. Davis, James A. 1979. “The Davis/Holland/Leinhardt Studies: An Overview.” Pp. 51-62 in Perspectives on Social Network Research, edited by Paul W. Holland and Samuel Leinhardt. New York: Academic Press.
  11. De Soto, Clinton B. 1960. “Learning a social structure.” Journal of Abnormal and Social Psychology 60: 417-421.
    [CROSSREF]
  12. Fine, Catherine G. 1993. “A Tactical Integrationist Perspective on the Treatment of Multiple Personality Disorder.” Pp. 135-153 in Clinical Perspectives on Multiple Personality Disorder, edited by Richard P. Kluft and Catherine G. Fine. Arlington, VA: American Psychiatric Publishing.
  13. Fuhse, Jan. 2016. Soziale Netzwerke. Konstanz: UVK Press.
  14. Hacking, Ian. 1995. Rewriting the Soul: Multiple Personality and the Sciences of Memory. Princeton, New Jersey: Princeton University Press.
  15. Handcock, Mark S. 2003. “Statistical Models for Social Networks: Inference and Degeneracy.” 229-240 in Dynamic Social Network Modeling and Analysis, edited by Ronald Breiger, Kathleen Carley and Philippa Pattison. Washington DC: National Academies Press.
  16. Holland, Paul W. and Samuel Leinhardt. 1970. “A Method for Detecting Structure in Sociometric Data.” American Journal of Sociology 76: 492-513.
    [CROSSREF]
  17. Holland, Paul W. and Samuel Leinhardt. 1976. “Local Structures in Social Networks.” Sociological Methodology 6: 1 – 45.
    [CROSSREF]
  18. Kant, Immanuel. 1950 [1787]. Critique of Pure Reason, translated by Norman Kemp Smith. London: Macmillan and Company.
  19. Kihlstrom, John F. 2005. “Dissociative Disorders.” Annual Review of Clinical Psychology 1: 227–53.
    [CROSSREF]
  20. Kleinfeld, Judith. 2002. “Could it Be a Big World After All? The ‘Six Degrees of Separation’ Myth.” Society 39: 61-66.
    [CROSSREF]
  21. Kluft, Richard P. and Catherine G. Fine. 1993. Clinical Perspectives on Multiple Personality Disorder. Arlington, VA: American Psychiatric Publishing.
  22. Krackhardt, David. 1987. “Cognitive Social Structures.” Social Networks 9: 109-134.
    [CROSSREF]
  23. Kuhns, Lisa M., M. Birkett, B. Mustanski, S.Q. Muth, C. Latkin, I. Ortiz-Estes and R. Garofalo. 2015. “Methods for Collection of Participant-Aided Sociograms for the Study of Social, Sexual and Substance-Using Networks Among Young Men who Have Sex with Men.” Connections 35/1. DOI: http://dx.doi.org/10.17266/35.1.1
    [CROSSREF] [URL]
  24. Lévi-Strauss, Claude. [1949] 1969. The Elementary Structures of Kinship, translated by James Harle Bell, John Richard von Sturmer, and Rodney Needham. Beacon Press: Boston.
  25. Martin, John Levi. 2009. Social Structures. Princeton: Princeton University Press.
  26. McLean, Theodocia. 2009. My Theodocia. Raleigh, North Carolina: Amazon.
  27. Milgram, Stanley. 1967. “The Small World Problem.” Psychology Today 2:60-67.
  28. Milo, R., N. Kashtan, S. Itzkovitz, M. E. J. Newman, and U. Alon. 2004. “On the uniform Generation of Random Graphs with Prescribed Degree Sequences.” arXiv:cond-mat/0312028 [cond-mat.stat-mech]
    [URL]
  29. Moody, James. 2004. “The Structure of a Social Science Collaboration Network.” American Sociological Review 69: 213-238.
    [CROSSREF]
  30. Orsini, Chiara et al. [11 co-authors]. 2015. “Quantifying Randomness in Real Networks.” Nature Communications 6:8627.
    [CROSSREF]
  31. Piaget, Jean. 1954. The Construction of Reality in the Child, translated by Margaret Cook. New York: Basic Books.
  32. Prince, Walter Franklin. 1917. “The Doris Case of Quintuple Personality.” The Journal of Abnormal Psychology 11:73-122.
    [CROSSREF]
  33. Putnam, Frank W. 1989. Diagnosis and Treatment of Multiple Personality Disorder. New York: Guilford Press.
  34. Ross, Colin A. and Pam Gahan. 1988. “Techniques in the Treatment of Multiple Personality Disorder.” American Jouranl of Psychotherapy 42:40-52.
    [CROSSREF]
  35. Smith, Jeffery. 2006. “Understanding DID Therapy.” Pp. 261-285 in A Fractured Mind: My Life with Multiple Personality Disorder. New York: Hachette Books.
  36. Tian, Xiaoli and Daniel A. Menchik. 2016. “On Violating One’s Own Privacy: N-adic Utterances and Inadvertent Disclosures in Online Venues.” Studies in Media and Communications 11: 3 – 30.
    [CROSSREF]
  37. Wasserman, Stanley, and Philippa Pattison. 1996. “Logit Models and Logistic Regressions for Social Networks: I. An Introduction to Markov Graphs and p*.” Psychometrika 61:401-425.
    [CROSSREF]
  38. Watts, Duncan J. 1999. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton: Princeton University Press.
  39. Wegner, David. 2002. The Illusion of Conscious Will. Cambridge, Mass.: Bradford Books.
  40. White, Harrison C., Scott A. Boorman, and Ronald L. Breiger. 1976. “Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions.” American Journal of Sociology 81:730-779.
    [CROSSREF]
  41. Whitehead, Harriet. 1987. Renunciation and Reformulation: A Study of Conversion in an American Sect. Ithaca: Cornell University Press.
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FIGURES & TABLES

Figure 1

Patricia’s 1990 Network

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Figure 2

Patricia’s 1992 Network

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Figure 3

Patricia’s 1993 Network

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Figure 4

Node Degree Distribution 1990

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Figure 5

Node Degree Distribution 1992

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Figure 6

Degree Heterophily for 1990, under dkl

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Figure 7

Degree Heterophily for 1992, under dkl

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Figure 8

Clustering by Degree and the dk2.1 Distribution for 1992

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Figure 9

Path Length by Distribution, 1993

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Figure 10

Clustering by Distribution, 1993

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Figure 11

Size of Largest Hollow Ring by Distribution, 1992

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REFERENCES

  1. Barnes, J. A. 1954. “Class and Committees in a Norwegian Island Parish.” Human Relations 7: 39-58.
    [CROSSREF]
  2. Bartlett, F.C. 1932. Remembering: A Study in Experimental and Social Psychology. Cambridge University Press.
  3. Blitzstein, Joseph and Persi Diaconis. 2011. “A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees.” Internet Mathematics 6(4); http://dx.doi.org/10.1080/15427951.2010.557277.
    [CROSSREF] [URL]
  4. Blount, G. 1986. “Dangerousness of Patients with Capgras Syndrome.” Nebraska Medical Journal 71: 207.
  5. Boltanski, Luc and Laurent Thévenot. 1983. “Finding one’s way in social space: A study based on Games.” Social Science Information 4: 631-680.
    [CROSSREF]
  6. Burt, Ronald S. 1992. Structural Holes: The Social Structure of Competition. Cambridge, Mass.: Harvard University Press.
  7. Bryant, Doris, Judy Kessler and Lynda Shirar. 1992. The Family Inside: Working With the Multiple. New York: Norton.
  8. Cohen, Barry M. and Carol Thayer Cox. 1995. Telling Without Talking: Art as a Window into the World of Multiple Personality. New York: Norton.
  9. David, Anthony, Roisin Kemp, Ladé Smith and Thomas Fahy. 1996. “Split Minds: Multiple Personality and Schizophrenia.” Pp. 122-146 in Method in Madness: Case Studies in Neuropsychiatry, edited by Peter W. Halligan and John C. Marshall.
  10. Davis, James A. 1979. “The Davis/Holland/Leinhardt Studies: An Overview.” Pp. 51-62 in Perspectives on Social Network Research, edited by Paul W. Holland and Samuel Leinhardt. New York: Academic Press.
  11. De Soto, Clinton B. 1960. “Learning a social structure.” Journal of Abnormal and Social Psychology 60: 417-421.
    [CROSSREF]
  12. Fine, Catherine G. 1993. “A Tactical Integrationist Perspective on the Treatment of Multiple Personality Disorder.” Pp. 135-153 in Clinical Perspectives on Multiple Personality Disorder, edited by Richard P. Kluft and Catherine G. Fine. Arlington, VA: American Psychiatric Publishing.
  13. Fuhse, Jan. 2016. Soziale Netzwerke. Konstanz: UVK Press.
  14. Hacking, Ian. 1995. Rewriting the Soul: Multiple Personality and the Sciences of Memory. Princeton, New Jersey: Princeton University Press.
  15. Handcock, Mark S. 2003. “Statistical Models for Social Networks: Inference and Degeneracy.” 229-240 in Dynamic Social Network Modeling and Analysis, edited by Ronald Breiger, Kathleen Carley and Philippa Pattison. Washington DC: National Academies Press.
  16. Holland, Paul W. and Samuel Leinhardt. 1970. “A Method for Detecting Structure in Sociometric Data.” American Journal of Sociology 76: 492-513.
    [CROSSREF]
  17. Holland, Paul W. and Samuel Leinhardt. 1976. “Local Structures in Social Networks.” Sociological Methodology 6: 1 – 45.
    [CROSSREF]
  18. Kant, Immanuel. 1950 [1787]. Critique of Pure Reason, translated by Norman Kemp Smith. London: Macmillan and Company.
  19. Kihlstrom, John F. 2005. “Dissociative Disorders.” Annual Review of Clinical Psychology 1: 227–53.
    [CROSSREF]
  20. Kleinfeld, Judith. 2002. “Could it Be a Big World After All? The ‘Six Degrees of Separation’ Myth.” Society 39: 61-66.
    [CROSSREF]
  21. Kluft, Richard P. and Catherine G. Fine. 1993. Clinical Perspectives on Multiple Personality Disorder. Arlington, VA: American Psychiatric Publishing.
  22. Krackhardt, David. 1987. “Cognitive Social Structures.” Social Networks 9: 109-134.
    [CROSSREF]
  23. Kuhns, Lisa M., M. Birkett, B. Mustanski, S.Q. Muth, C. Latkin, I. Ortiz-Estes and R. Garofalo. 2015. “Methods for Collection of Participant-Aided Sociograms for the Study of Social, Sexual and Substance-Using Networks Among Young Men who Have Sex with Men.” Connections 35/1. DOI: http://dx.doi.org/10.17266/35.1.1
    [CROSSREF] [URL]
  24. Lévi-Strauss, Claude. [1949] 1969. The Elementary Structures of Kinship, translated by James Harle Bell, John Richard von Sturmer, and Rodney Needham. Beacon Press: Boston.
  25. Martin, John Levi. 2009. Social Structures. Princeton: Princeton University Press.
  26. McLean, Theodocia. 2009. My Theodocia. Raleigh, North Carolina: Amazon.
  27. Milgram, Stanley. 1967. “The Small World Problem.” Psychology Today 2:60-67.
  28. Milo, R., N. Kashtan, S. Itzkovitz, M. E. J. Newman, and U. Alon. 2004. “On the uniform Generation of Random Graphs with Prescribed Degree Sequences.” arXiv:cond-mat/0312028 [cond-mat.stat-mech]
    [URL]
  29. Moody, James. 2004. “The Structure of a Social Science Collaboration Network.” American Sociological Review 69: 213-238.
    [CROSSREF]
  30. Orsini, Chiara et al. [11 co-authors]. 2015. “Quantifying Randomness in Real Networks.” Nature Communications 6:8627.
    [CROSSREF]
  31. Piaget, Jean. 1954. The Construction of Reality in the Child, translated by Margaret Cook. New York: Basic Books.
  32. Prince, Walter Franklin. 1917. “The Doris Case of Quintuple Personality.” The Journal of Abnormal Psychology 11:73-122.
    [CROSSREF]
  33. Putnam, Frank W. 1989. Diagnosis and Treatment of Multiple Personality Disorder. New York: Guilford Press.
  34. Ross, Colin A. and Pam Gahan. 1988. “Techniques in the Treatment of Multiple Personality Disorder.” American Jouranl of Psychotherapy 42:40-52.
    [CROSSREF]
  35. Smith, Jeffery. 2006. “Understanding DID Therapy.” Pp. 261-285 in A Fractured Mind: My Life with Multiple Personality Disorder. New York: Hachette Books.
  36. Tian, Xiaoli and Daniel A. Menchik. 2016. “On Violating One’s Own Privacy: N-adic Utterances and Inadvertent Disclosures in Online Venues.” Studies in Media and Communications 11: 3 – 30.
    [CROSSREF]
  37. Wasserman, Stanley, and Philippa Pattison. 1996. “Logit Models and Logistic Regressions for Social Networks: I. An Introduction to Markov Graphs and p*.” Psychometrika 61:401-425.
    [CROSSREF]
  38. Watts, Duncan J. 1999. Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton: Princeton University Press.
  39. Wegner, David. 2002. The Illusion of Conscious Will. Cambridge, Mass.: Bradford Books.
  40. White, Harrison C., Scott A. Boorman, and Ronald L. Breiger. 1976. “Social Structure from Multiple Networks. I. Blockmodels of Roles and Positions.” American Journal of Sociology 81:730-779.
    [CROSSREF]
  41. Whitehead, Harriet. 1987. Renunciation and Reformulation: A Study of Conversion in an American Sect. Ithaca: Cornell University Press.

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