Examples of Ties in the following topics:

 Degree centrality measures might be criticized because they only take into account the immediate ties that an actor has, or the ties of the actor's neighbors, rather than indirect ties to all others.
 One actor might be tied to a large number of others, but those others might be rather disconnected from the network as a whole.

 Members of one group may prefer to have ties only within their group; members of another group might prefer to have ties only outside of their group.
 Members of the "other" group have a low probability of being tied to one another (.143) or to "capitalists" (.143), but somewhat stronger ties to "workers" (.250).
 Within group ties among capitalist interest groups (group 2) are very slightly less common (.01) than heterogeneous group ties (again, not significant).
 Ties among interest groups representing workers (group 3) however, are dramatically more prevalent (.81) than ties within heterogeneous pairs.
 CorePeriphery 2 offers a more relaxed block model in which the core remains densely tied within itself, but is allowed to have ties with the periphery.

 The EI (external  internal) index takes the number of ties of group members to outsiders, subtracts the number of ties to other group members, and divides by the total number of ties.
 The resulting index ranges from 1 (all ties are internal to the group) to +1 (all ties are external to the group).
 A large number of trials are run in which the blocking of groups is maintained, and the overall density of ties is maintained, but the actual ties are randomly distributed.
 The densities off the main diagonal (outgroup ties) appear to be slightly more prevalent than the densities on the main diagonal (ingroup ties).
 Next, we see the numbers of internal ties (14, or 22%) and external ties (50, or 78%) that yield a raw (not rescaled) EI index of +.563.

 A common interest in looking at directed dyadic relationships is the extent to which ties are reciprocated.
 In large populations, usually most actors have no direct ties to most other actors, and it may be more sensible to focus on the degree of reciprocity among pairs that have any ties.
 Here, two such ties (A to B and B to A) are a reciprocated structure among the six possible ties (AB, BA, AC, CA, BC, CA) or a reciprocity of .333.
 Analysts usually focus, instead, on the number of ties that are involved in reciprocal relations relative to the total number of actual ties (not possible ties).
 That is, of all the relations in the graph, 69% are parts of reciprocated ties.

 The other half of the design of network data has to do with what ties or relations are to be measured for the selected nodes.
 In many network studies, all of the ties of a given type among all of the selected nodes are studied  that is, a census is conducted.
 But, sometimes different approaches are used (because they are less expensive, or because of a need to generalize) that sample ties.
 There is also a second kind of sampling of ties that always occurs in network data.
 Any set of actors might be connected by many different kinds of ties and relations (e.g. students in a classroom might like or dislike each other, they might play together or not, they might share food or not, etc.).

 A graph (sometimes called a sociogram) is composed of nodes (or actors or points) connected by edges (or relations or ties).
 Directed ties are represented with arrows, bondedtie relations are represented with line segments.
 Directed ties may be reciprocated (A chooses B and B chooses A); such ties can be represented with a doubleheaded arrow.
 The strength of ties among actors in a graph may be nominal or binary (represents presence or absence of a tie); signed (represents a negative tie, a positive tie, or no tie); ordinal (represents whether the tie is the strongest, next strongest, etc.); or valued (measured on an interval or ratio level).

 How many are weak ties?
 Social networks are composed of nodes and ties.
 Ties are assessed in terms of strength.
 Strong ties, like family bonds are called strong ties.
 Smaller, tighter networks composed of strong ties behave differently than larger, looser networks of weak ties.

 Actors who have more ties to other actors may be advantaged positions.
 Because they have many ties, they may have alternative ways to satisfy needs, and hence are less dependent on other individuals.
 If an actor receives many ties, they are often said to be prominent, or to have high prestige.
 That is, many other actors seek to direct ties to them, and this may indicate their importance.
 Simply counting the number of inties and outties of the nodes suggests that certain actors are more "central" here (e.g. 2, 5, 7).

 Individual actors may have many or few ties.
 Individuals may be "sources" of ties, "sinks" (actors that receive ties, but don't send them), or both.
 The number and kinds of ties that actors have are a basis for similarity or dissimilarity to other actors  and hence to possible differentiation and stratification.
 The number and kinds of ties that actors have are keys to determining how much their embeddedness in the network constrains their behavior, and the range of opportunities, influence, and power that they have.

 If we have measured the ties among actors with values (strengths, closeness, probabilities, etc.) density is usually defined as the sum of the values of all ties divided by the number of possible ties.
 That is, with valued data, density is usually defined as the average strength of ties across all possible (not all actual) ties.
 That is, of the six possible directed ties among actors 1, 3, and 5, four are actually present (we have ignored the diagonal  which is the most common approach).
 Governmental generalists (block 1) have quite dense in and out ties to one another, and to the other populations; nongovernment generalists (block 2) have outties among themselves and with block 1, and have high densities of inties with all three subpopulations.