Notes from Kadushin, Charles. 2012. Understanding Social Networks: Theories, Concepts, and Findings. New York, NY: Oxford University Press.

Chapter 1:

Human beings have always been defined, in one way or another by networks:

• Kinship and family relations
• Neighborhoods, villages, and cities are crisscrossed with networks of obligations and relationships.
• Picking up the mail when one is away, help with fixing the lawn mower, or recommendations for good restaurants.

Some suggest that urban Americans are becoming more and more socially isolated:

• Robert Putnam. 2000. Bowling Alone: The Collapse and Revival of American Community. New York, NY: Simon and Schuster.

However, what we are seeing may be best describe as a movement away from place-based communities to an interlinked web of connections

Networks:

• "A network is simply a set of relations between objects which could be people, organizations, nations, items found in a Google search, brain cells, or electrical transformers." (pages 3-4)
• Everyone is Connected, or could be. If you know 100 people (Facebook friends), and each of them knows 100 others--then in 2 steps, you are connected to 10,000. In three steps, 1,000,000, and in 4 steps 100,000,00--and so on.
• Connections provide access to resources:
  • Jobs
  • Home repair
  • Help
  • Social capital
• Social network analysis reveals what is hidden in plain sight. When you buy something online, most sites tell you what other things people who also bought that object went on to purchase. How often do you follow their lead?
  
• Networks as Conduits--wanted (valued resources) and unwanted (obesity, smoking) flows. (Christakis and Fowler 2007)

Chapter 2: Basic Network Concepts, Part I

What Is a Network?

• "...a network is a set of relationships. More formally, a network contains a set of objects (in mathematical terms, nodes) and a mapping or description of relations between the objects or nodes. The simplest network contains two objects, 1 and 2, and one relationship that links them. Nodes 1 and 2, for example, might be people, and the relationship that links them might be as simple as standing in the same room. If 1 is in the same room as 2, then 2 is in the same room as 1." (page 14)
  
  
• Directionality
  • Mutuality (reciprocity)
  • Anti-symmetric (liking, power, etc.)
  • Multiplex relationships
• Flows and exchanges
  • Transitive relationships (balance: A likes B and B likes C; implies A likes C)
  • Network distance: degree of separation (steps)
  • A balanced and mutual network--all nodes are directly linked.
  • The simple network of three units is called a triad. This simple network turns out to be the building block of more complex relations.
  • Sociogram (Jacob Moreno)(example)

Core questions:

• What are the conditions that make it more or less likely that a path will exist between two nodes?
• How likely is it that the nodes will have the same attributes?
• How likely is it that nodes will be reciprocally or mutually related to one another?

Three kinds of networks:

1. Ego-centric-connected via a single node
2. Socio­centric--connected within a broader social/organizational context (students in a classroom)
3. Open-system networks--boundaries not necessarily clear.

Propinquity: for all networks, geographical closeness is associated with a greater likelihood of connection.

• Co-location
• Co-presence (relationship)
  

Homophily

• People (or other social units) with similar characteristics are more likely to be connected.
• People who are connected are more likely to have similar characteristics.
• Feedback: overtime homophily increases-in relationships.
• "Birds of a feather flock together."

Individual-Level Homophily

• Lazarsfeld and Merton: status-homophily (ascribed and achieved) and value-homophily: homogeneity
• Relevant to the sociology of class, gender, ethnicity, and nationality as well as cultural values.
• There are two kinds of causes of homophily.
  1. 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.
  2. Structural location. Two nodes may have the same attributes because both operate in the same arena, and again, vice versa. While similar pairs tend to form a relationship, the availability of similar attributes is a function of social structure.
• 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.
• The principle of homophily exemplifies the tendency of social networks to be "unfair" and makes "social engineering" to counter prejudice and segregation more difficult.

Homophily and 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.
• Element of power. (page 20)

Dyads and Mutuality

• Two nodes relate to each other:
  • Reciprocity
  • Little to no power asymmetry
• Mutuality is strongly affected by the social and cultural structure within which the dyads are embedded.
  • Husband-wife (changing)
  • Doctor-patient
• Mutuality begins early in life and is a key factor in human development (childhood friendships).
• Organizational mutuality: police and counseling centers dealing with illicit drug use--who sends people to whom?
• Most studies assert: the greater the similarity of the attributes of the pairs, the greater the likelihood of there being a flow between them (see homophily, above).
  

Balance and Triads

• Triads are the beginnings of a "society" that is independent of the ties between a dyad.
• Simmel: triads contain (at least the the probability of) direct and indirect relationships, mediation, division and side-taking.
• "Balance Hypothesis"-- "a friend of my friend is a friend of mine" and "an enemy of my friend is an enemy of mine." Beyond intuition, this can be more formalized as: "In the case of three entities, a balanced state exists if all three relations are positive in all respects, or if two are negative and one is positive" (Heider 1946, 110).
• 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 2009, 45). 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."
• There are actually 16 possible configurations of triads.

Chapter 3: Basic Network Concepts, Part II
WHOLE SOCIAL NETWORKS

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." However, sociograms that contain more than ten nodes are hard to grasp and subject to different interpretations depending on who is "watching." Analytic concepts and methods that account for the entire network and describe and summarize various aspects of it are necessary.

Distributions of network properties are the first set of key descriptors:

1. The number of dyads and triads in the network.
2. Density, the number of connections contained within the network
3. Structural Holes, a category concerned with the lack of connections.
• Strength of Weak Ties, hypothesizes that important things flow from people with whom one has limited connections.
4. Popularity and Centrality demonstrate that some nodes have more connections than others and those connections serve as links to other nodes.
5. The Distance across the network between nodes. The radius of distances from any given node is an important descriptor.
   • For people, those nodes directly connected with a focal node comprise the Inter-personal Environment.
   • The number of nodes in an interpersonal environment is related to the key concept of Small World,which describes the relatively small distances that link a given node to all the nodes in a given network.
6. Multiplexity recognizes that there may be many networks that connect, in different ways, the same nodes.
7. Position or Role is a concept that is not distributional but invokes how nodes relate to other nodes in the network.
   

Dyads and Triads:

• Core elements of network complexity and intensity (not the individual).

Density:

• Density is defined as the number of direct actual connections divided by the number of possible direct connections in a network.
• 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 villages have greater density than modern cities, and people tend to know one another in many contexts-as relatives, coworkers, church attendees, and so forth. Given the human limitation on the number of sustainable connections, smaller networks will have greater density. It is easier to know everyone in a small group than in a large community. In comparing different net­ works in terms of density, one therefore has to take into account their size.
  

Structural Holes:

• Density is focused on connection, structural holes shifts attention to the lack of connection.
• A network of two or more clusters connected by a single node suggests a structural hole. If the connecting node was not present, the networks collapses.
• The single connecting node has significance as the "broker" (a position of power) in the network.

Weak Ties:

"The Strength of Weak Ties" is the title of an article by Mark Granovetter (1973) 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 1967). Like structural holes, "weak ties" also focuses on holes in the network. The most authoritative statement of the idea is Granovetter's 1982 reprise:

[O]ur acquaintances ("weak ties') are less likely to be socially involved with one another than are our dose friends ("strong ties'). Thus the set of people made up of any individual and his or her acquaintances will constitute allow-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 will be densely knit (many of the possible lines present). ...Ego will have a collection of close friends, most of whom are in touch with one another-a dense "dump" of social structure. Ego will [also] have a collection of acquaintances, few of whom know one another. Each of these acquaintances, how­ ever, is likely to have dose friends in his or her own right and therefore to be enmeshed in a closely knit dump of social structure, but one different from Ego's ...These dumps would not ...be connected with one another at all were it not for the existence of weak ties. (Granovetter 1982, 105-106)

• Weak ties facilitate the flow of information from otherwise-distant parts of a network. Individuals with few weak ties will be deprived of information from distant parts of the social system and will be confined to the provincial news and views of their dose friends.
• 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 will 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.
  

Complications to the analysis of weak ties.

• 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?
• The critical function of weak ties is one of bridges between network segments. 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 1983, 229).
• "(1) something flows through these bridges- they actually serve as conduits bearing information and influence to groups they otherwise would not get, and (2) whatever it is that flows actually plays some important role in the social life of individuals, groups, and societies" (ibid 228-229).
  • A strong tie can absorb most costs and pass on something (information concerning a job) than a weak tie--if the individual in the position has need of the information passed on.

"Popularity" or Centrality:

Popularity can be broken down into several different ideas relating to centrality:

• The number of connections a particular node has (degree). When the network is directed (not reciprocal), there is an indegree, number of "votes" received, and an outdegree, number of chokes made.
• 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 entity is popular among the popular.
• "Betweenness"-- the idea of a switching point. The person or organization that serves as a connector or a switching point can be very important, above and beyond their "popularity."
• Centrality is important--leadership. If centrality is distributed (independence), no strong leader and individual satisfaction is high. If a particular node dominates in centrality--leadership emerges and it is likely only the central node will have high satisfaction.
  

Distance:

• The number of steps (degrees) connecting two nodes in the network.
• Formally, 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 to 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.
• 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. So one might count the first step as important, the next step as less important, and so on.
• Some things, such as computer viruses (not "social" in the human sense), spread unadulterated through many steps.
• Reach or connectedness: links between (and size of) "first-order" zone and second, third, fourth, etc. Snowball effect.

Size of the Interpersonal Environment:

• Interpersonal environment or the first-order zone varies from about 100 to 5,000 persons.
  • Classic village societies ("everyone knows everyone else"): small interpersonal environment
  • Contemporary urban societies: social class, ethnic and racial variation and barriers.
  • Organizations have these zones, too.
• The alleged "six degrees of separation" modified by variation in connections and overlap between shared connections.
• Three Degree of Influence Rule: influence (from us and to us) ripples out, but beyond 3 degrees of separation, little effect (Christakis and Fowler. 2009. Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. New York, NY: Little, Brown, and Co. page 28).

Multiplexity (multiple connections between nodes):

• Role multiplexity: two nodes may occupy more than one position that ties them together (friends and co-workers):
  • Common in small interpersonal environments.
  • Role Set set issue in larger systems (segmentation).
• Content multiplexity: different "flows" between nodes.
• Mechanical versus Organic Solidarity (Durkheim).
• Access and trust: impact on organization and economic developments.
• Formal and Informal relationships.
  

Roles and Positions

• Named Positions and Roles (statuses): core elements of social structure--primary statuses: kinship--role expectations and prohibitions.
• Informal Positions and Relationships (friends--symmetrical relationships)(page 39)
• Informal Relations and Hierarchies (power, prestige-contagion)
• Embeddedness
  • Relationships and networks are embedded within formal arrangements (even informal relationships and networks).
  • Networks are influenced by and related to cultural and social structural frameworks.
  • Information and ideas are also shaped by networks that amplify and transmit the ideas and the information.
  • Power in America: legislative mechanism, but not all legislators are the same, as well as the role of lobbyists. (page 40)
    
• Observed Roles:
  • "Emic" (insider ideas--who is recognized by participants as a leader)
  • "Etic" (ideas imputed to a culture by observers--who occupies a leadership position based on network analysis)
    • Unnamed positions or roles are those that observers ascribe to a structure which may or may not be so described and noted by the "natives."
    • Roles, statuses, or positions that have names (emic) 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.

Chapter 4: Network Basics, part 3 Network Segmentation

Separate whole networks into smaller meaningful segments.

As with network position, there are emic and etic clusters or groups.

Emic groups are named and recognized by the "natives."

• These can range from a club or gang with a name such as "Hell's Angels," to a corporation such as "General Electric," or a legal government entity such as "New York State."
• A group or cluster has "members." That is, there are individuals who are members of Hell's Angels or General Electric, and organizations or groups who are members of "GE," such as "GE Capital"
  1. Members know that they are members of the group.
  2. Others know that they are members of the group and can identify them as such.
  3. Members interact with one another more than they interact with non-members (usually, not always)

Etic segments of a network are those that are identified by observers. Examples are the "C's"2: clusters, cliques, clacks, circles, cabals, (but not clubs-they are emic), coalitions, and also some non-"C's" such as "group" and "block."

PRIMARY GROUPS, CLIQUES, AND CLUSTERS

The concept of primary group was introduced by Charles Cooley in 1909:

By primary groups are characterized by intimate face-to-face association and cooperation.

• Fundamental in forming the social nature and ideals of the individual.
• The result of intimate association, psychologically, is a certain fusion of individualities in a common whole, so that one's very self, for many purposes at least, is the common life and purpose of the group.
• Perhaps the simplest way of describing this wholeness is by saying that it is a "we"; it involves the sort of sympathy and mutual identification for which "we" is the natural expression. One lives in the feeling of the whole and finds the chief aims of his will in that feeling. (Cooley 1909, 23)
• Cooley notes that members of a primary group identify themselves with it. (etic view)

Clusters

• A formal term, clusters have some of the structured characteristics of named groups or organizations
• there may be a clear hierarchy of positions within the cluster.
• In most formal analyses, clusters do not overlap. That is, a node cannot simultaneously be a member of two clusters, though it is a possibility.
• Large-scale social network patterns and clusters are inherently messy matters--
  • Need formal organization
  • Oftentimes, members may not pay much attention to the "organization chart".
    

SEGMENTING NETWORKS ON THE BASIS OF COHESION

Cohesiveness defines "cliques."

• All members of a clique "choose" or are linked to one another (Wasserman and Faust 1997, 254).
• In clique interaction, since all persons interact with one another, the persons can not be distinguished from one another (Martin 2009, 29), They are mathematically equivalent to one another.
• The volume of mutuality in relationships is simply too great to sustain in real life. This designation also means that a person can be a member of only one clique: membership in two cliques would require that all the relationships be mutual and result in the collapse of the two into a single clique.

RESISTANCE TO DISRUPTION

White and Harary (2001) utilize the sociological concept of group cohesion. In a further elaboration (Moody and White 2003, 106) observe, "A collectivity is structurally cohesive to the extent that the social relations of its members hold it together." Furthermore, "A group is structurally cohesive to the extent that multiple independent relational paths among all pairs of members hold it together ...The strongest cohesive groups are those in which every person is directly connected to every other person (cliques), though this level of cohesion is rarely observed except in small primary groups."

The cohesiveness of a group can be gauged by looking at two processes that are the obverse of one another.

1. Cohesion: A group is cohesive to the extent that the members are pulled together when confronted with disruptive forces.
2. Adhesion: Cohesiveness can be estimated by seeing what happens to the disconnectedness of a group when one or more members (nodes) are removed or, keeping the same number of nodes, when one or more paths or connections between the members or nodes are removed.
3. A group may have low density of relations between its members and be relatively resistant to disruption, while an equally dense group may be less resistant to disruption, less cohesive in these terms. Especially interesting is the possibility that there are groups with sparse connectedness that can actually be quite cohesive in terms of their resistance to forces that would break them up. The method creates nested hierarchical trees but also allows for overlaps between groups within those trees.

STRUCTURAL SIMILARITY AND STRUCTURAL EQUIVALENCE

The other way of partitioning or segmenting networks utilizes the master idea of reaching out to other nodes and examining the pattern of a node's relations with the other nodes in the network, rather than looking for cohesion in terms of relations between the nodes. Nodes that have similar patterns of relationships with other nodes are grouped together. This idea is called structural similarity (Burt 1992; Borgatti and Everett 1992). Managers may have similar patterns in their relations to employees in their units. Structural equivalence, a more strict formulation, is defined as nodes that are connected to the same other nodes in identical ways. To be structurally equivalent, two managers would have to have the same relationships to the same employees, an unlikely situation. Since identical relations are relatively infrequent, there are ways of modeling "ideal" patterns and then assessing how well these patterns fit the data (Doreian, Batagelj, and Ferligoj 2005) or how similar they are (Breiger, Boorman, and Arabie 1975). The method was first developed by White, Boorman, and Breiger (1976) and was called "blockmodeling." Blockmodels partition networks into non-overlapping segments-an advantage or a disadvantage depending on what one is trying to do. The modeling aspect comes from the fact that blocks so constructed are abstractions from the data and can be algebraically manipulated.' Clusters or blocks can be represented by a matrix of i's and o's. In the following example (table41), there are two blocks, A and B, each consisting of a number of nodes. The 1's represent the presence of a relationship; the o's the absence of a relationship. The tables are read in terms of the rows relating to the columns. In the first row, block A relates to block A and to block B. In the second row, B relates to A but not to itself. Remember, these are not individual nodes, but clusters of nodes.5

Core/Periphery Structures

Core/periphery structures are the simplest forms of network segmentation. The reason core/periphery structures are so familiar to us is that we have all experienced them, starting from our days in a playground. There were kids who were on the inside while others were on the outside. This patterning continues through grade school, high school, and throughout life. However, even in this apparently simple structure, there are different patterns to explore.

There are several other kinds of elite cores." There is a "caucus" type of core. Breiger (1979) suggests that this type of cluster can be applied to the community power literature. Those active in block A "run" the community and do not pay much attention to the others who do not have political relationships (though they might have other kinds of relationships) with each other or with the core. The core does not take account of the periphery, and the periphery has no relationship with the core or with others.
If we consider directed graphs, those that are not necessarily symmetrical, then we can have the Groucho Marx situation as in his famous line, "I sent the club [the Friars Club] a wire stating, 'Please accept my resignation. I don't want to belong to any dub that will accept me as a member'" (Marx 1959, 321).

More generally, this is a diffusion model from a core: The core has what other nodes want, so they look to it. Unlike a trading situation, the core does not want anything from the periphery. The relation is not symmetric.

There can be a situation, shown in table 4.6 in which A remains the elite in that A relates only to other N.s, but B also has some density of relating to other B's, and also to A. Breiger calls this situation one of "deference."A wants nothing from B, but the B's have something to offer to one another.

To complete the logic of core/periphery, there can be the following kind of relation­ ships (table 4.7), in which the last come first and "the meek inherit the earth."

This simply turns the caucus or the elite core blockmodel on its head, assuming that the B block has fewer power attributes. We suspect that in reality this model is largely empirically absent. The "meek" blockmodel (table 4.7), however, suggests a proposition about core/ periphery networks.Cores possess whatever attributes are most valued by the network. While this seems like a simple tautology, it is not and may be the result of extremely complex processes. 1he network is about relationships and flows, not about the attri­ butes of the nodes. This proposition says that in core/periphery structures, the valua­ tion of the attributes is related to the structure.8 1he proposition does not state which comes first, however one must ask, do the nodes that have the most of what is valued come to be the core, or do the nodes that already have the most of what is valued impose their values on others who have less and confine them to the periphery? This proposi­ tion was first formally noted in terms ofleadership and norms by George Homans in his reinterpretation of the "Norton Street Gang" in The Human Group (Homans 1950). Leaders were said to embody more of the norms of the group than the followers. Simi­ larly, the core in world/systems theory has the more advanced economy; political core elites have more power; the core in overlapping corporate boards of governors have more control; and the core in cultural diffusion has cultural hegemony. 1his proposition will be elaborated upon in the chapters that follow.

Thus far it seems that network analysis is a scheme that merely enforces the status quo. 1hat is, the network embodies the values of the system, and the core/periphery model allows for no change. Yet there is one logical possibility that has not yet been examined. In terms of the network relations in the political arena, there could be a situation of two dusters or caucuses polarizing the community (table 4.8). They relate to themselves but not to one another.

This polarizing situation occurs in a modern community in which there is some overlap of circles in an unstable situation. Coleman describes this kind of structure as the second stage in community conflict after an issue is introduced (Coleman 1957). This blockrnodel implies the following idea: network polarization is central to social change. Social transformation leads to polarization of networks, or, the reverse, polar­ ization of networks leads to social change in terms of norms, values, and other social structures. The karate club, above, was an example of polarization. The ramifications of this model for social change will be discussed in the chapters that follow.

In the real world there are rarely two chokes, and blockmodels can be complicated by incorporating additional blocks, C, D, . . . N. The models above that depict just two blocks are intended to present the basic idea of core/periphery models-the most simple of networks. Even they can be complex.

Bow best to partition networks, especially large ones, remains one of the frontiers of network analysis, though much progress has been made recently (see chapter 8). Whole large networks are messy matters, but the network field has gone a long way from talking about social relations and networks as metaphors to analyzing them and building testable models. The following chapters will review and expand upon some of the things we have learned.

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