Types of Ties
The term “tie” encompasses relational phenomena of very different types. In practice, the kinds of ties that network theorists tend to focus on can be categorized into two basic types: states and events. One type of event tie is a transaction. We want to know if, for example, an AQ Khan will sell nuclear technology to Al Qaeda.[1] It is an interaction between nodes. When something flows or diffuses from one node to another, it is because of such an interaction. This is a discrete event that occurs between two parties.
A very different kind of tie is a friendship between two people. Although the onset of such a tie might be viewed as a discrete event, the tie itself is best thought of as a relational state. During the period it is active, the tie has continuity over time. This is not to say the tie is permanent but rather that it has an open-ended persistence. Examples of state-type ties include role-based relations (e.g., friend of; boss of), cognitive/perceptual relations (e.g., recognizes; knows the skills of) and affective relations (e.g., likes; hates). Relational states can be thought of as the conditions or context within which events occur.
We expect that a relational state such as friendship or trust enables certain events, such as transactions, to occur. Similarly, we expect relational events to create relational states. Certainly repeated relational events, such as having lunch together, can forge a relational state, much as students walking on a college campus create a path in the grass which then attracts more walkers.
More technically, any relational event creates a certain relational state of the form “once did X with”, as in pairs of nodes that “have spoken to each other” or “have dated”. Another way to think of these is in terms of co-participation. If three people go out to lunch together, then each is related to each other by a relational state of having once participated lunched with each other. More generally, if relational events can be classed as members of type, then we can count the number of relational events that pairs of nodes have co-participated in.
Table 1 summarizes a more detailed typology of social ties. It should be noted we distinguish between social ties and the larger category of relational phenomena, which includes things like physical distance and flows between nodes. Table 2 summarizes this expanded set of relational phenomena. In the table, “correlations” refers to a class of relational phenoma that includes physical distance, co-membership in groups (e.g., organizations, tribes), co-participation in events (e.g., political rallies), and similarities on attributes (e.g., same gender, same phone brand). Correlations often serve as relational conditions or opportunities that enable social ties to form (or in the breach, prevent them from forming). On the right side of the table are “flows” which refer to the traffic that flows along the roads provided by social ties. Hence, as a result of interaction, a node receives tangible or intangible goods from another. We divided flows into two basic categories, replicable and transferable. Transferable flows are material objects that are transferred from node to node and can only be in one place at one time. Replicable flows are things like information which can be passed from node to node but remain with the source node..
Table 1. Typology of Social Ties
Table 2. Full typology of Relational Phenomena
There is a subtle difference between co-participation, such as having attended the same event, and a relational event. For example, if A and B both attended the ball, there is a co-participation relation between them. But this is different from A and B going with each other, which is a more exclusive relation. In the former case, there is an event, and there is a relational state that results from the event, but there is no relational event. In the latter case, there is a relational event (going to the ball with each other) and a relational state we can abstract from it (“have ever been to the ball with each other”).
An interesting type of relational event is flow. A flow is the movement or transfer of something from one node to another via that is enabled by the relational state between them. For example, two cities are connected by a road, and over time we see cars moving from one city to the other along the road. Each car trip is a relational event – in this case, a flow.
Flows are a kind of contagion. Contagion occurs when, as a result of the tie between them, the state of node A changes the state of node B. Consider, for example, a conversation between A and B about a math problem, which results in B thinking that the solution is X. Note that A may not have given B the answer per se, but rather might have explained the underlying principles so that B could come to the answer X. Note also that A may in fact have a different answer than B, but B’s answer is still a result of their interaction. Contagion implies lack of independence in states, but not sameness.
A flow is an outcome of a relational tie. In the case of cars moving between cities, it is an outcome of the relational state (road) that exists between them. In the case of a sexually transmitted disease, it is most immediately the result of an interaction (sex) which may have been enabled by a social relation (“going together”).
In general, we associate flows with sameness of states, but it should be noted that it is sameness of B at time T with the state of A at time T-1. This is clearly true when what is flowing can only be in one place at a time, and flowing implies transference or movement from one location to another, as in a car moving from A to B. In that case, what is at B used to be at A, but is not any longer. For things that copy when they flow, such as information or a virus, it is still the case that the proper comparison is with the details of B’s virus at time T with the details of A’s virus at time T-1, because the virus at A may be mutating over time, so that at time T the state of A is not the same as the state of B, and this is not evidence against flow.
Valence
Different ties have different implications for individuals. For example, role-based ties such as friendship or various kinds of kinship ties entail certain rights and responsibilities that the nodes have in relation to each other. These in turn would have implications for the kinds of relational events that could be expected to occur between them. A high resolution model of tie formation would include these different implications for different kinds of ties.
For our purposes, however, simpler is better. One simplification is to classify all types of ties in terms of valence, as in positive and negative. This would include both relational states (e.g., ally of, enemy of) and relational events (e.g., defends, attacks).
Direction
Relational phenomena like co-participation in events, co-membership in groups, and sibling relationships are undirected, meaning that a tie is not from one node to the other, but is simply between them. In short, the relation does not have direction. Colloquially we tend to think of this as all ties being reciprocated (so that if A attends the same event as B then B attends the same event as A) but in fact reciprocation is a different concept. In contrast, ties like “lends money to,” “sells weapons to”, and “has trust in” have clear direction from one actor to another. Directed ties may or may not be reciprocated. Directed relationships such as “seek career advice from” are not likely to be reciprocated as they often occur as directed ties from a novice to someone with more work experience. Whereas other directed relationships such as “lend emotional support to” are more likely to be reciprocated at a later date (e.g., I help you out today with the expectation that I can count on you for help in the future).
Value
While it is convenient to regard ties as present or absent, it is more realistic in many cases to regard ties have a quantitative value. Values are especially natural in the case of correlational phenomena, such as physical distance between nodes. For co-membership and co-participation we can count the number of groups or events the nodes have in common, often weighting inversely by the size of these groups or events. In the case of relational states, this usually refers to the strength of the tie or the capacity of the tie to handle flows. Values can also be used to capture the duration of a relational state. In the case of relational events (and particularly categories of relational events), we often use value to capture frequencies of recurrence. For correlations
[1] According to news reports, Khan did try to see weapons to Saddam Hussein, but was turned down because the Iraqis thought it might be a CIA trap.