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He selects material that serves as basic building blocks and examples of best practices that will allow the reader to understand and evaluate new developments as they emerge. Understanding Social Networks will be useful to social scientists who encounter social network research in their reading, students new to the network field, as well as managers, marketers, and others who constantly encounter social networks in their work. Individual Members of Networks. Whole Social Networks. Network Segmentation. The Basic Building Blocks. Common attitudes can be based on patterns of relationships Erickson Numerous studies have documented the tendency towards homophily in a variety of social networks McPherson, Smith-Lovin, and Cook But a critical research and theoretical question is which characteristics, attributes, or activities are selected in a given situation to be salient candidates for homophily.

For example, the extent to which the situation values "race" or defines it in terms of skin color will affect whether common characteristics such as skin color will be related to children's choice of one another as friends in a classroom situation Hallinan ; Hallinan and Williams Because of the principle of homophily, social network analysis thus almost invariably involves the sociology of class, gender, ethnicity, and nationality as well as cultural values. Some of the sorting out and clustering of networks is of course the result of visible attributes, but some is the result of less visible ones.

To make the less visible more visible, dating and matching services offer checklists through which they attempt to bring people together. Propinquity can also be more broadly defined as being in the same place at the same time. There is a distinction between co-location, which puts people simply within range of one another, and co-presence, which implies a social relationship that is within the framework of a social institution or social structure Zhao and Elesh Common interests e.

Studies of elites show that persons are more likely to have a connection, relationship, or friendship if they went to the same prep school at the same time Domhoff Of course, these individuals may merely share an "old school" tie they went to the same school but at different times , in which case we are talking about homophily, a different kind of propinquity.

There are two kinds of causes of homophily. Common norms or values may bring nodes with common attributes together, or the reverse, common attributes and contacts may lead to common norms, and this holds true for both individuals and collectivities Burt , For example, a study of adolescent girls found that students belonging to the same clique tended to have similar scores on various measures of behaviors such as binge eating, alcohol use, dietary restraint, and so on. But we do not know whether adolescent girls hang around together because they share similar habits, or they have become similar to each other while hanging around with one another Hutchinson and Raspee In general, research on homophily investigates the conditions under which homophily is likely to occurwhich factors in a social system encourage which kinds of similarities and leads to particular ties McPherson, Smith-Lovin, and Cook This is even more complex than it seems because homophily is a process.

To reiterate, if people hang out together they tend to have the same attitudes, and if they have the same attitudes, they tend to hang out together Erickson Chicken-and-egg situations always create difficulties, and a major part of Lazarsfeld and Merton's original formulation was devoted to Lazarsfeld's essentially unsuccessful attempts to sort this out. Homophily Homophily from the Greek, "love of the same" is a concept introduced into social theory by Lazarsfeld and Merton [] that embeds a folk proposition:. The converse is also true: if two people are connected, then they are more likely to have common characteristics or attributes.

There is also an implied. Two nodes may have the same attributes because both operate in the same arena, and again, vice versa Feld and Carter While similar pairs tend to form a relationship, the availability of similar attributes is a function of social structure. I am more likely to find people interested in solving mathematical problems in a physics class than in a class on English literature. But people drawn to mathematics are more likely to choose a physics class that an English class. The feedback between network structure and individual preference thus becomes especially noticeable over time.

In sum, if people flock together, it appears that there are four processes involved: 1 the same kinds of people come together; 2 people influence one another and in the process become alike; 3 people can end up in the"same place; 4 and once they are in the same place, the very place influences them to become alike. For example, in one study of social network engineering and race, a police academy attempted to facilitate racial integration by populating squads with a selection of recruits that reflected the demographics of the larger cohort Conti and Doreian The academy also instituted fixed seating.

Review of Kadushin, Charles: Understanding Social Networks: Theories, Concepts, and Findings

As observed and surveyed over the training period, squads "worked to increase levels of social knowledge within and between races through time as well as the level of friendship at the end of the academy. Thefixedseating arrangement worked in the same fashion but as a weaker force. Social knowledge and friendship were highest for pairs of recruits in the same squad and were adjacent in the fixed seatingboth within and between races" ibid.

Interaction led to greater understanding, but not to a complete elimination of conflict around race: "expunging underlying attitudes regarding race-is another matter. Throughout the academy, an underlying tension regarding race existed and was expressed with racist remarks recorded as part of the ethnographic data " Ibid. Homophily and Collectivities Hypotheses about homophily are straightforward for individual persons, but somewhat more complex when it comes to collectivities. At the organizational level, whether similarity leads to a greater likelihood of a tie depends on the kind of a connection, as well as the on the industry.

But common characteristics and geographic propinquity do not necessarily lead to a tie. For example, Ford does not sell cars to General Motors. On the other hand, when engineers and managers move from one company to another, a tie develops. Basic Network Concepts, Pari I 21 between the automobile companies. Similarly, software firms in Silicon Valley cultivate ties to one another through their practice of regularly licensing software to one another and also exchanging personnel.

Geographic co-location is of course covered under the heading of propinquity, but through the principle of "external economy," it also leads to homophily via structural co-location. External economies, as the name implies, are "the economies that a-firm can obtain through the use of facilities or services 'external' to itself" Hoover and Vernon This leads to the classic situation of "birds of a feather flocking together" to take advantage of readily available services and hence lower transaction costs.

It is no accident that firms that compete with one another and thus have very similar attributes are also geographically close Uzzi We will have more to say about this principle when we discuss social circles of organizations. The corporate examples suggest that power in a relationship is not irrelevant. Given that there is a dyad formed by virtue of homophily, and that the dyad connection itself creates greater homophily, what is the role of power or mutuality in the dyad?

We often observe that in any relationship at any time one of the pair has an advantage over the other. When are the relationships equal; when is there mutuality? Dyads and Mutuality We have seen that in directed graphs or networks, there can be four possible relationships: none at all they are not connected , A relates to B, B relates to A, and A and B both relate to one another.

We are concerned here with the fourth relationship, reciprocity or mutuality. The concept "of mutuality implies first, that relations are reciprocal, that is, they involve a give and take between the two parties; and second, that power or asymmetry in the relationship is of little or no consequence. Mutuality is strongly affected by the social and cultural structure within which the dyads are embedded. For example, in elementary school, girls are more likely to reciprocate friendship choice than are boys. Girls may be more socialized to emphasize personal relationships therefore develop more intimate friendships Shrum, Cheek, and Hunter The doctor-patient relationship can be a close one, though guided by professional norms.

Recent developments in psychoanalysis, however, urge a more mutual relationship between therapist and patient Mitchell The American husband-wife relationship is another one in which norms of mutuality have been changing, though to be sure women still do more housework and have greater responsibility for child rearing. Under what conditions, in what kinds of networks, can we expect that nodes will have a mutual relationship?

One can try and address this question by looking at the likelihood that a particular network or social system will be composed of more or fewer mutual relationships than one might expect at random Mandel ; Wasserman and Faust Mutuality begins early in life and is a key factor in human development. While at the level of individuals it may be difficult to sort out mutuality, at the organizational level this task may be easier. Organizations can share an attributetwo organizations that confront illegal drug problems, for example.

In this respect, the police and psychiatric clinics can be said to be in the same network. Then we examine the nature of flows between them. Do the police send people to psychiatric clinics; do the clinics send people to the police? If both are true, how does this reciprocal relationship work out in practice? Is there more than one relationship between the police and psychiatric clinics? For example, do they "exchange" clients a flow , and are they both members of the mayor's task force on fighting drug addiction a shared connection ; and if so, how does this multiplex relationship affect them?

Answers to these apparently very simple questions can result in complex analyses of the roles of different organizations in dealing with drug problems. Just as a reminder, there are also relations between units larger than organizations. There is an entire branch of economics that deals with trade relations between nations Krugman and Obstfeld For example, contrary to the theory that argues that the hierarchical structure between core and peripheral countries are becoming more and more solidified, the reciprocity between countries in the global telecom network was found to have increased between and Monge and Matei There are a large range of propositions and studies about pairs of relations, most of which assert that the greater the similarity of the attributes of the pairs, the greater the likelihood of there being a flow between them see homophily, above.

While this may be obvious, consider that most "coalition building" consists of cheating mutual flows between pairs that do not share many attributes. There is a major movement in public healtlj and in drug- and alcohol-addiction-prevention programs that attempts to build community coalitions in an effort to have an impact on drug and alcohol consumption. Although "obvious" to network analysts who understand that bringing pairs together in the long term when they have quite different characteristics is difficult and rare, this elementary fact of pair relationships is apparently poorly understood.

Balance and Triads As noted, network analysis really begins with triads, for they are the beginnings of a "society" that is independent of the ties between a dyad:. In respect to its sociological destiny This peculiar closeness between the two is most clearly revealed if the dyad is contrasted with the triad [in Simmel's German, 'associations of three']Where three elements, A, B, C, constitute a group, there is, in addition to the direct relationship between A and B, for instance, their indirect one, which is derived from their common relation to C Discords between two parties which they themselves cannot remedy, are accommodated by the third or by absorption in a comprehensive whole Yet Simmel , In Simmel's view, the third can be non-partisan and a mediator, but can also be "the Tertius Gaudens" the third who enjoys; Simmel , The third can line up with one of the two others and thereby gain his or her own advantage or can act as a broker between them and make a broker's profit.

This latter possibility will be taken up at greater length when we consider Burt's "structural hole" argument Burti Simmel also observed that the rriost certain way of compromising a secret between two people is to add a third to the "secret. One important set of ideas hinges on the balance between the three members of a triad and leads to the classic "Balance Hypothesis.

For example, the earlier network illustrating a triad shows all three relationships to be positive.


Heider further contends based on the principles of Gestalt psychology that there is a tendency over time toward balance; "[i]f a not balanced state exists, then forces towards this state will arise. Martin suggests that given two emotional states love and hatred and extremely rational participants, there must be strong institutional support for the balance to emerge, for the simple reason that the "laws" of balance assume a reactivity that is the opposite of what would consider rational.

Take the principle, "my enemy's friend is my enemy. It is a poor sort of enemy who allows himself to be guided by this maxim" Martin , Martin explains that if A and B are enemies, it is good strategy for A to try to make friends with B's friend C and all of B's friends, thus leaving B completely isolated. Whatever the chosen strategy, triads are analogous to molecules in a periodic table of elements.

While there are only a handful of elements found in nature, molecules combine to form complex chemical structures, according to certain rules in the case of triads, rules include balance, transitivity, homophily, and circles or foci, among others : "The triad census is thus a periodic table of social elements' and similarly able to categorize and build social structures. We offer the figure for reference because of the great amount of workman has been focused on this, the most elementary network.

Most of these analyses are beyond the scope of this introduction. StiE, as we shall see, there are some interesting consequences to the possible arrangements of the triads and their nested dyads. In the next chapter on whole networks, we will show how different arrangements affect the interpretation of cohesiveness in a small club.

The first character in the triad name gives the number of mutual dyads. For example, there is one in triad number 3. The second character gives the number of asymmetric dyads, for example, 1 in triad number 2. The third character gives the number of null dyads, that is, no connection between pairs, as in the very first triad in which none of. The fourth character, if present, distinguishes between triads. Vijlrhidi are otherwise identical. For example, there are two triads, number 9 and umber Number 9 is Transitive and number 10 Cyclical.

Numbers 7 and 8 look alike except that in 7 the asymmetric pair has a Downward arrow or connection sign, and 8 has an Upward arrow. The arrangements may seem obscure, but the census or count of configurations can be compared with the chance distributions of these configurations in any network and yield jmportant insights about the network. From the balance hypothesis, it follows : : that friends are likely to agree about a third partyif one of them likes a third,party, :] both will like that person.

And close friends agree more strongly about a third party than j!. Configurations numbers 7 and 8 that conform to this hypothesis should be, statistically more frequent in a social network than configurations that do not. This balance tends to be supported in a wide variety of social networks ' in which the nodes are people Wasserman and Faust, International alliances also seem to foEow the hypothesis Antal, Krapivsky, and Redner 20o6. Another property of For example, triad number 9 contains one transitive relationship, triad 12 contains two, and triad 16 contains six transitive relationships.

In contrast, triad 6 is intransitive. Statistical tests "are very supportive of the proposition that interpersonal choices tend to be transitive" Wasserman and Faust , Intransitive triads are very rare.

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Nonetheless, balance is only one theory about choice in a network and does have its limitations by postulating rigorous rules for relations that in messy social life do not always hold. Social circles and foci of activities see earlier discussion are other reasons for relationships.

While the distribution of triads seems at first to be a limited idea, the prevalence of different combinations of triads. We shall see in chapter 5 how transitivity defines the boundaries of a smaU group. Indeed, the plan of this book foUows the heuristic that networks are built up from smaller components. We observed previously that tendencies toward reciprocity start early. So too do transitivity and balance. In the same study of preschoolers and social networks cited earlier, "children were more likely to select others as play partners when those ties increased.

Where We Are Now We began with some simple definitions. A network is a set of nodes ahd a map showing the relationships between the nodes. The simplest network is a dyadL'Relationships in a dyad can be undirected, mutual, or directed. When there is more than one relationship between a pair, such as coworkers and friends, it is called multiplex. Relationships are transitive when what holds for A to B, also holds for B to C.

Triads begin to introduce a true social system. FinaEy, a description of social networks does more than merely list friends or supporters but rather reveals the extent of connections between them. SociaEy interesting aspects of networks occur when homophily and propinquity are introduced. Sure, "birds of a feather flock together" but how this phenomenon occurs for individuals and for coEectivities and under what circumstances forms the basis of social analysis, whether the subject be friendship patterns, corporate overlap, or international trade.

EspeciaEy interesting is sorting out feedback and "chicken-and-egg" issues. People become more similar when they hang out together; but they hang out together in the first place because they are similar. While there are major tendencies for balance in triads, other principles may also be at play.

Groups and individuals may strategize to avoid the consequences of balance and try to make friends with enemies. People come together in different foci or social circles in which not everyone is symmetricaUy related to the others and yet they are a relatively cohesive unit. Although triads are perhaps the analogue of molecules for networks, there is an even smaEer unitthe dyad. Whole networks consist of many dyadsthe basic building block of networks with which we began.

Each connected triad is, as we have seen, composed of three dyadswithin the pair the choices or connections are either reciprocated or not. A further fundamental aspect of a whole network is centrality or popularity. Then there is the density of the whole network: the number of direct connections or ties that exist, divided by the number of possible direct ties.

Size is always important. SmaE groups tend to have high density, whereas large networks, though connected, tend to have low density. The email network of a university may connect aE the students and faculty, but most of these are not directly connected so the email network is relatively sparse and has low density. This is typical of large networks. The distribution of reciprocated or unreciprocated dyads, centrality, and overall network density may account for most of the variance in the distribution of triads in human sociability networks Faust 20O7.

This brings us directly to a more detailed discussion of whole networks in the next chapter. Key concepts that informed the discussion were homophily the tendency of pairs of nodes to share the same characteristics and balance the tendency of the third in a triad to share or have a characteristic that complements the other two.

Important as these ideas are, the essence of social network theory and analysis lies in a consideration of an entire network, to which we now turn. A sociogram, the graph or diagram of a whole network, examples of which were shown in the first chapter, is one way to understand an entire network. As Yogi Berra reputedly said, "You can observe a lot by watching. Distributions of network properties are the first set of key descriptors and include the number of dyads and triads in the network.

Other distributions discussed in this chapter include: Density, the number of connections contained within the network, and its opposite, Structural Holes, a category concerned with the lack of connections. A related concept, Strength of Weak Ties, hypothesizes that important things flow from people with whom one has limited connections. Popularity and Centrality demonstrate that some nodes have more connections than others and those connections serve as links to other nodes.

Other distributions describe the Distance across the network between nodes. The radius of distances from any given node is an important descriptor. In terms of people, those nodes V. Multiplexity recognizes that there may be many networks that connect, in different ways, the same nodes. Finally, Position or Role is a concept that is not distributional but invokes how nodes relate to other nodes in the network. As will be seen, position is the most traditionally "sociological" of the concepts I will be presenting and serves as a link to the next chapter that takes up how whole networks can be partitioned into coherent segments.

Distributional concepts help illuminate the sociogram that follows.

Charles Kadushin, Understanding Social Networks

In a muchanalyzed example of a small group, anthropologist Wayne Zachary carefully observed a karate club comprised of 34 members for more than two years. In this example, we are not concerned with how the network came into being but rather the consequences of its structure.

The sociogram was drawn by a computer program, Pajek Nooy, Mrvar, and Batagelj and presented by White and Harary It depicts the network of friendships among the club members figure. The connections are based on the observations of the anthropologist and not on the setf reports of the members.

There are 1, symmetric dyads in the network triad type in chapter 2, figure 2. A computer program randomly shuffled the network of 34 people and the symmetric connections between them, caEed "edges" in graph theory. In each shuffle, the program counted the number of symmetric dyads. The number of dyads was much greater than would have been found by chance.

In terms of fuE triads, club member number 17 on the far left is directly connected with 6 and 7; they constitute a symmetric triad. Another is 6,7, and 1. Also, 11,5, and 1 is a symmetric triad. There are 45 such triads in the entire network triad type in chapter 2,figure2 , also far more than expected by chance. The dyads and triads calculations were not made by hand, an effort that would have been tedious and likely to have resulted in many mistakes. Rather, these and later calculations that iEustrate distribution concepts in this sociogram, were accomphshed by me with a widely used computer program, UCINET 6 Borgatti, Everett, and Freeman DENSITY Density is defined as, the number of direct actual connections divided by the number of possible direct connections in a network.

The karate club network is obviously densely connected. The overall density is 0. There seem to be at least two parts to the networkthe right side and left sideand within each part the density is obviously greater than the average. We will discuss partitioning a network into "natural" groups in chapter 4. Density is at the heart of community, social support, and high visibility when people in a network can see what others are doing and monitor and sanction their behavior. Density facilitates the transmission of ideas, rumors, and diseases.

Other things being equal, the greater the density, the more likely is a network to be considered a cohesive community, a source of social support, and an effective transmitter. Classic agricultural communities or viEages have greater density than modern cities, and people tend to know one another in many contextsas relatives, coworkers, church attendees, and so forth. Given the human limitation on the number of sustainable connections, smaEer networks will have greater density. It is easier to know everyone in a smaE group than in a large community. In comparing different networks in terms of density, one therefore has to take into account their size.

The cohesiveness of blocks in social networks: N6de connectivity and conditional density. Sociological Methodology ,figure Copyright John Wiley and Sons, Density is based on the idea of connection. But one can turn the idea on its head and reprinted by permission. Each cluster is totally connected, that is, each of their members is said to be structurally equivalent to each other.

However, the members' only link to one another is "Ego. The important implications of structural holes and the role of Ego as a "broker" will be considered in greater detail in chapter 5. WEAK TIES "The strength of weak ties" is the title of an article by Mark Granovetter that has achieved almost as much fame and certainly more citations than the more popularly known "small world" described by Stanley Milgram in his Psychology Today article Milgram The most authoritative statement of the idea is Granovetter's reprise: [0]ur acquaintances "weak ties' are less Hkely to be socially involved with one another than are our close friends "strong ties".

Thus the set of people made up of any individual and his or her acquaintances wiE constitute a low-density network one in which many of the possible ties are absent , whereas the set consisting of the same individual and his or her close friends wiE be densely knit many of the possible lines present. Ego wiE have a collection of close friends, most of whom are in touch with one anothera dense "clump" of social structure. Ego will [also] have a coEection of acquaintances, few of whom know one another.

Each of these acquaintances, however, is likely to have close friends in his or her own right and therefore to be enmeshed in a closely knit clump of social structure, but one different from Ego's These clumps would not Granovetter , [italics in original] Weak ties have several interesting consequences Granovetter , First, weak ties facilitate the flow of information from otherwise-distant parts of a network. Individuals with few weak ties wiE be deprived of information from distant parts of the social system and wiE be confined to the provincial news and views of their close friends.

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Second, weak ties help to integrate social systems. The macroscopic side of this communication argument is that social systems lacking in weak ties will be fragmented and incoherent. New ideas wiE spread slowly, scientific endeavors will be handicapped, and subgroups that are separated by race, ethnicity, geography, or other characteristics will have difficulty reaching a modus vivendi. There are various complications to the analysis of weak ties. First, the definition of what constitutes a weak tie or relationship can be somewhat slippery. Is it the length of time one knows someone else, the frequency of interaction, the subjective "closeness" one feels, or whether the others one is connected with are defined as relatives, friends, or acquaintances?

Second, it is important to understand that the critical function of weak ties is one of bridges between network segments.

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As Granovetter puts it, "The importance of weak ties is asserted to be that they are disproportionately likely to be bridges as compared to strong ties, which should be underrepresented in that role. This does not preclude the possibility that most weak ties have no such function" Granovetter , Third, it must be the case that " 1 something flows through these bridgesthey actuaEy serve as conduits bearing information and influence to groups they otherwise would not get, and 2 whatever it is that flows actuaEy plays some important role in the social life of individuals, groups, and societies" ibid.

Aflowcan occur only under some circumstances. Passing along information or exercising influence should not be too costly to the weak tie that constitutes the bridge; otherwise, strong ties that are wiEing to bear the cost wiE be more effective in making the bridge. For example, if a mere acquaintance knows about a job the original context of Granovetter's study , and the acquaintance does not need the job himself or herself, then there is little cost in passing along the information.

It would take a strong tie to pass along information that might cause a loss to the person passing it along. It is obvious in the karate club that persons 1 and 34 have great centraUty. Many lines radiate from them or go to them, because friendship is reciprocal. The sheer number of connections is caEed "degree. When the network is directed not reciprocal , there is an indegree, number of "votes" received, and an outdegree, number of choices made. Almost aE networks have nodes or persons with higher degrees than other members of the networks, whether the topic is friendship or corporate connections to banks.

An interesting variation on the focus on the number of votes is the source of the votes. A node is more popular or powerful if it receives nominations, or indegrees, from nodes that themselves have high degree. The individual or'fentity is popular among the popular. There are various measures of power or prominence that take this factor into account.

In the karate club, whEe nodes 1 and 34 have the highest degree and the most power, nodes 3 and 33, because they receive nominations from 1 and 34 and others with high degree, also score fairly high on power. An inspection of the network shows that 1 and 34 are in the middle of things. One can get to other members via these leaders. This is called "betweenness" Freeman There are various methods for measuring betweenness, but aE are based on the idea of a switching point. The person or organization that serves as a conhector or a switching point can be very important, above and beyond their "popularity.

In the karate club, although 16 and 34 each have almost the same degree, 1 has a higher betweenness score. Node 1 connects the cluster on the extreme left with the rest of the club, making node 1 a bridger or broker. Centrality has many substantive implications. A classic series of experiments with networks of various shapes showed that "where centrality and hence, independence are evenly distributed, there will be no leader, many errors, high activity, slow organization, and high satisfaction" Leavitt , On the other hand, when a network was shaped in a "wheel" patternso called because individual persons, the spokes, were coordinated by a central personthe organization was efficient, but only the person E in the center of figure 3.

Not only are there many direct connections in the karate club network, but also many indirect ones. For example, 17 is directly connected with 7 and indirectly connected through 7 and 6 to 1 in a second step. While the symmetric dyads and triads are by definition transitive see chapter 2 , it is not assumed that indirect connections, such as between 17 to 1, are transitive. That is, 17 is not necessarily a friend of 1 or 1 a friend bf That two-step connection is the shortest connection of 17 with 1.

But also, because this is a dense network, 17 can get to 1 in three steps via 5 or via AE the nodes,are eventually connected with one another through paths of various lengths. The longest path with direct connections is of length 5, and there are 16 of those. This is a compact network whose average distance is 2. Not so incidentally, the computer program that drew the network placed 17 and 15 at opposite sides of the diagram.

FormaUy, the distance between two nodes is defined as the length of the shortest path via the edges or binary connections between nodes. This is called geodesic distance. Shortest paths are efficient, but there are also consequences to inefficient or redundant paths in which there are many ways to get from one node td another. Redundancy, as noted in connection with density, makes sense in the diffusion of norms, attitudes, or values.

One might have to hear the same thing from several different sources until it takes root. Then too, in terms of diffusion, we might want to discount a source that is several steps removed because messages might get garbled as they pass from one node to another that is not transitive.

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So one might count the first step as important, the next step as less important, and so on. On the other hand, some things, such as computer viruses not "social" in the human sense , spread unadulterated through many steps. The set of nodes directly linked to any given node is caEed the first-order zone Barnes ; Mitchell The nodes two steps removed from a focal node are caEed the second-order zone, and so on.

When the first-order zone is about individual persons, the term "interpersonal environment" is often used Rossi ; WaEace In graph theory, this is caEed the "neighborhood.

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The friends of the friends in the first-order zone are reached in only two steps. If the first-order zone is large, then many friends of friends can be reached one of the principles of Facebook. If the friends in the second-order zone are not the same ones as in the first-order zone, then Ego has a large reach indeed. Reach or connectedness the famous "six degrees of separation" was studied by Milgram in his "smaU world" experiments MEgram Larger whole networks such as cities or communities would be ideal subjects for the study of distance, popularity, and density.

However, we have not been. A possible alternative means of getting information about networks is to study members of the first-order zone of a sample of respondents through the use of "name generators" Wellman This system produces egonetworks, that is, networks centered about a particular individual.

source url In a widely utilized data set, the General Social Survey in asked respondents to name up to five others with whom they "discussed important matters. The study might include a number of different name generators, and more than five individuals might be pursued. Although this ego network might seem to be a limited application of network ideas, the data so generated has been extremely powerful and the source of a number of insights into social networks that will be referred to throughout this book.

One can measure the density and the social characteristics of the ego's interpersonal environment, that is, the dyadic relationships between ego and each of the persons mentioned. One can also try separately to survey the persons mentioned in a "snowball" technique, thereby moving out a number of steps from ego. Size of the Interpersonal Environment The number of individuals in the interpersonal environment or the first-order zone varies from about to 5, persons, depending on how it is measured for example, people you know by name and the type of society in which the focal person is embedded Bernard et al.

In general, as we wiE see, in classic village societies "everyone knows everyone else," so the number of steps from one person to any other is minimal. Village societies are also relatively small and confined so that the first-order zone may be no more than about local persons Boissevain , thus limiting the number of persons who can be directly reached.

In contemporary urban societies, professionals and middle-class people have a larger first-order zone than blue-coEar and lower class people Kadushin and Jones On the other hand, in these societies there maybe serious barriers across class and ethnic lines, making for greater distances between persons in different classes and ethnicities WeEman a. The issue is a complex one and wiE be taken up later. Organizations too have first-order, second-order, and tertiary zones, as suggested by the concept of external economy described in the previous chapterthose aspects, of an organization that it rehes upon to survive and thrive but which are not formaUy a part of the organization.

The ne'twork of part suppliers for automobile manufacturers is part of their external economy, but so is the absorption of the costs of carbon emissions by the rest of society. These matters wiE be discussed when we come to organizations and overlapping circles. Suppose everyone in the United States knew other people and that each set of was uniquenone of the people you know are known by, say, your brother or sister. Then, each of the people you know in turn knows unique others, and they each know others, and so on Pool and Kochen , Five hundred people raised to the power of three is 12,,, much greater than the size of the U.

Under such circumstances, getting out of one's immediate circle becomes more difficult. Social structure, as Pool and Kochen demonstrated, reduces the number of unique individuals in the iteration of steps; and therefore, the expansion to a large population takes more steps or links. For example, it is more difficult for whites to reach African Americans. This topic will be analyzed when we discuss social circles of individuals. Despite the theoretical number of two to three steps between any two persons in the United States, experiments done by Stanley MEgram and his students in the s estimated the actual number of steps to be six, reached through five intervening persons MEgram ,; Travers and MEgram , hence the popular phrase, "six degrees of separation.

InMEgram's original experiments, most people were not able or were unwiEing to make the requested connections. A recent experiment using the internet found that few of the chains were actuaEy completed and concluded that, although in principle people were connected, the actual successes depended on their motivations and incentives Dodds, Muhamad, and Watts In MEgram's experiments, people were asked to reach a target person in a distant city by means of a person most likely to know the target person on a first-name basis.

The experiment worked like a chain letter. The number of steps was higher than the theoretical number because there were social structural barriers to network linkages. In the first experiment, MEgram reported that links between men and women were much less frequent than same-sex linkages, a finding repeated in the recent experiment.

SimEarly, there were barriers between social classes. Hence, personal agency or motivation became a factor in establishing Enkages. Organizations, too, vary in the extent to which they actively seek to relate to other organizations and are skEled in this endeavor. Multiplexity Thus far, only single-stranded ties have been formaEy considered, though we have given some examples of multiple connections.

The members of the karate club had. That is, their relationships were multiplex. The members could relate to one another in eight different contexts such as going to the same classes or hanging out together in a bar across the street from the campus Zachary , The karate club network depicted earlier reported any relationship originating in any one of the eight settings.

The density of the network based on any one relationship would obviously be less than shown above. In most situations, there are multiple connections between nodes. Multiplexity is related to the concept of homophEy discussed in chapter 2, for the bundling of particular kinds of ties is hardly random and foEows the laws of homophily of position that we have already discussed. Multiplexity has been used in the network literature in two related senses: one, sometimes caEed role multiplexity Beggs, Haines, and Hurlbert , refers to the possibility that two nodes occupy more than one position that ties them together, typicaEy, the situation described earlier in which two nodes have an organizational relationship, say "supervisor" and "assistant" to the supervisor , but are also friends.

ClassicaEy, this occurs in viEage societies in which people are simultaneously kin,, workers on the same farm, members of the same religious cult, and the host of shifting roles common to village economies in which tasks are largelyfiEedby part-time specialists in which the blacksmith may also be the head of a clan, the godfather to a number of persons, and a local inteEectual sage. Boissevain offers this proposition: "Because the activity fields in this small community overlap and the same actors play different roles to the same audience, we may also expect high multiplexity" Boissevain , In complex non-viEage societies, roles may become bundled in a somewhat different way.

Merton caEs attention to "role sets," the set of relationships that ensue because one occupies a given role what he calls status , an idea that Rose Coser further elaborates Coser ; Merton b. A school teacher relates to students, parents, a school administrator, the Board of Education, and so on. This is the role set that goes with the status of teacher. This role set can of course be analyzed using the formal tools of network analysis, especiaEy those that work with "ego networks. The secondsense refers to the possibEity that, as a result of having a given role relationship, say "coworker," there are a number of different flows between a pair of persons, for example, advice, friendship, and work on common tasks Lazega and Pattison This has been caEed "content multiplexity" Beggs, Haines, and Hurlbert Further, the same tie, for example advice, can have a number of different kinds of ideas flowing through it: a solution to a problem, a reformulation of the problem, information about solutions to the problem, reaffirmation of an already identified solution, and the credibEity of a proposed solution Cross, Borgatti, and Parker Attention here is directed to the different consequences of these multipleflowsand how they Enk or conflict under different circumstances.

The concept of multiplexity has an important place in sociological theory. First, as we have aEuded to, other things being equal, multiplexity is arguably an important indicator of the presence of folk or village society forms of organization and even rural-urban difference in modern America. Second, given the multiple bases upon which relationships can be formed within a community, multiplexity has an important role in theorizing about economic forms.

Padgett shows that over two centuries to in Florence, the birthplace of financial capitalism, commercial banking firms were formed on four distinct bases: first on the basis of family and patrilineage, next on the basis of guilds, then on the basis of social class, and in the last period, on the basis of patronage Padgett ; Padgett and Ansell The extent that access and trust are available to bolster economic relations is a consequence of multiplex relationships of different types. For example, ethnic enclaves have been shown to be advantageous to certain kinds of ethnic businesses in part because of the multiplexity of relationships Portes and Sensenbrenner Trust, so established by virtue of the ethnic tie, also has global aspects Tilly The effect of ethnic enclaves on labor market outcomes, however, is greater for less skilled workers than for professionals Edin, Fredriksson, and Aslund Trust among the French financial elite was bolstered by multiplex relations of party, neighborhood, and friendship Kadushin Third, a very substantial proportion of the literature on organizations is concerned with the relationship between ties based on formal positions in the organization and those based on informal relationships discussed earlier.

The consequences of formal and informal modes of relations within organizations hinges on the how these multiplex relations are construed in different settings. Informal relations were first identified as loyalties that impeded production Homans Others have found informal relations augment formal relations by facilitating the accomplishment of various tasks Lazega and Pattison There can be complex relations between formal and informal relations that encourage mentoring or prevent the acquisition of values appropriate to a given organizational role Podolny and Baron While multiplex relations can be described qualitatively and discursively, and one can often get an intuitive sense of what is involved in multiple relations, more precise characterizations of the consequences and causes of different permutations of ties has proven to be a difficult task.

The possible combinations of ties can be quite daunting, and the factors that lead to one sort of tie may not have the same force on another type of tie. Multiple flows between positions as well as multiple simultaneous positions can enhance a relationship and buEd trust, for example, friendship between supervisor and assistant or between poEtical leaders. On the other hand, depending on the circumstances, the same friendship can create a conflict of interest or even the possibility of fraud Baker and FaEcner Obviously, much depends on the context, and the context can be structural or cultural or both.

Merton's role set theory concentrates on the possible negative consequences of multiple role relations and suggests various ways conflict can be managed or alleviated. But the difficulty of quantitatively testing hypotheses on multiplexity has limited formal theorizing in this extremely interesting field. There is another aspect of whole networks: the type of relationship between nodes. Let us caE this relationship a role or a position. There is a classic literature in sociology and anthropology about positions and roles for example, Linton ; Parsons ; Merton b , and there are network analogues and equivalents.

First, there are those that are ordained by the social system with very specific names, typically kinship names such as mother, father, chEdren, aunts, uncles, and cousins, or organizational positions such as boss-worker. These relationships are typicaEy asymmetric. Second, there are those relationships that are more loosely and generically named friend, neighbor, acquaintance, or coworker and are more typically symmetric.

The network properties of each named relationship, as opposed to generic relationships, are quite dissimEar and have been studied in very different ways. But both types of relationships lead to puzzles and surprises. Although this may be confusing, the concept of "role" is often used both for the position as well as for the relationship between positions. The logical complications of kin relationships can be quite complex, and formal network mathematics can help to specify the implications of such matters as bilateral cross-cousin marriages in which "one's wife is also both Mother's Brother's and Father's Sister's Daughter" White , Anthropologists have tended to gather networks of named relationships in almost all-of their fieldwork, in part because they can do so with only a limited knowledge of the local language.

It is one matter to gather the data about the relationships, and another to understand their implications, a"s controversies in the literature about the causes and consequences of cross-cousin marriage suggest Homans and Schneider ; Levi-Strauss ; Needham Named relations are of course far from being the whole story, for anthropologists have gathered massive data about the official names of the positions, but not necessarily systematic data about the actual relationships between the positions. We wiE not enter into the details of kinship analysis and the predictions that can be developed from using network analysis to describe kinship structures mathematicaEy.

But the principle illustrated by kinship is the association, or lack of it, between formal named and instituted relationships and those that are "informal" or unanticipated. More generaEy, almost aE network analysis involves at some point comparing the network mandated by culture and the social system to networks created and negotiated by people in the process of trying to manage and work the "system.

To take this extreme point of view is to deny the weight of tradition and habit, but most of aE, to deny that concepts and names have consequences with which people daily struggle. In Crime and Custom in Savage Society, Malinowski [], gives a poignant example of the problems of a young man who wanted to marry a woman who was, according to kinship rules, forbidden to him. Because Malinowski spent all of World War I in rife Trobriand Islands, and therefore had considerable time to observe the local population, he was able to compare the rules to the way they were actuaEy carried out.

I found the breach "of exogamyas regards intercourse not marriage is by no means a rare occurrence, and public opinion is lenient, though decidedly hypocritical" ibid. While Malinowski observed many examples of the breach of exogamy and "[m]ost of my informants would not only admit but actually did boast about having committed this offence or that of adultery He was aware of "only two or three cases of marriage within the clan.

Informal relations are thus not independent of formally defined or culturally named positions. The informal exists in reference to, or even in opposition to, the formal relationships. It is as if the non-prescribed paths or relationships or exchanges are "draped" upon a scaffolding of the formal relationships. The instituted or prescribed relations are always in some way, even negatively, "taken into account.

Informal Relations and Hierarchies There are network equivalents to power or status positions. Hierarchy in networks can be seen as a transitive tree or pyramid structure as in figure 3. The relationships are transitive in a power structure because A can command or instruct B, who can command F. A's command, of B is binding on F. They are asymmetric because B cannot command or instruct A. The tree structure as depicted has no horizontal connectionsB, C, and D, for example, are not connected,.

One needs to study aE these systems carefuEy-the kinship, the organizaf tional, and the national legislatureto uncover the informal connections. Nonethe less, these connections are related to the mandates and functions of the formal In real-world networks, there are often horizontal connections so that rank or status can "leak" or flow by the principle of homophilya node can acquire the prestige of those she or he hangs out with, as any social climber knows Podolny , chapter 2.

Further, in real-world trees there may not be symmetry of command, but there may be symmetry of information because information may flow up and down the levels. Figure 3. But formal hierarchy is often not the whole story. In a large manufacturing organization I observed, there were formal hierarchical relationships that defined the positions in the organizationthe "organizational chart" similar to the stylized hierarchical chart shown above. When critical decisions were made, individuals often "skipped levels" and enEsted support above the level of their immediate superior.

True, this is an "informal system" for making decisions. But the person chosen as the one higher in rank than the one supposedly entrusted with the decision was hardly picked at random. Which brings us to the issue of embeddedness. Embeddedness means a number of different things to different students of networks.

AE agree, however, that networks are influenced by and related to cultural and social structural frameworks. And the converse holds true as weE. Information and ideas are affected not only by relations between pairs, but are also responsive to being part of dense networks that amplify and transmit the ideas and the information. A good example of embeddedness is the constant struggle to determine how power in America actuaEy works.

In American national politics, channels for creating legislation are prescribed by law. But certain committee members and lobbyists count for more than others and are the ones who criticaEy determine what a new law is likely to. Anthropologists distinguish "emic" and "etic" concepts. Emic ideas are those that "insiders" to a culture use, and "etic" ideas or concepts are those that observers impute to the culture or find useful in describing it. The relationships between the individuals and the central role played by the coordinating figure in the "wheel" communications structure described earlier were imposed by the design of the experiment.

Yet in the wheel configuration, most experimental subjects, when asked about "the organization of your group," were able to describe it. On the other hand, subjects in other configurations were not able to do so Leavitt There is an important literature in the network field that refers to "roles," as discovered through network analysis methods that create partitions of whole networks White, Boorman, and Breiger But these partitions are not necessarily defined as normative named roles by the participants in the network.

Positions that have "structural similarity," as discovered through network analysis, can be described as occupying a role or a status, though this may not be so noticed or conceptualized by participants in the structure. Whether or not the roles are emic or etic does, however, have important consequences.

Roles, statuses, or positions that have names are much more likely to have a longer life than roles or positions that have been ascribed to a structure as a result of network analyses. Persons in an organization who occupy a position discovered through network analysis that allows them "structural autonomy"that is, the abEity to act as brokers between persons who otherwise would not be Unked see the karate club example, above are not very Ekely to hold that position a year later Burt In contrast, a person who holds a named position is more likely to continue in that position.

To summarize the matter of positions and roles. Network relations can be prescribed by values, organization, and institutions. Often, when relations are prescribed, they are given a name. Relational names are very important in predicting the forms that networks take. But the prescribed relations are only part of the story, since relationships are further elaborated on the base of the prescribed. Under many conditions, the elaborations become instituted and so become prescribed, and another round of elaboration begins. Since most people know the prescriptions, one "charm" of network analysis.

But these revelations are only part of the story. Even the prescribed relationships are sufficiently complex so that participants in society see only the relationships that immediately surround them in the first-order zone and are rarely aware of the implications of second-order zones. Participants are unable to visualize, much less model, the entire system.