Notes on the introduction to “Networks of Collective Action”, by Edward O. Laumann and Franz U. Pappi. 1976, Academic Press, New York, NY

p.6
Structural Analysis

Network symmetry vs. asymmetry
This connotes whether a given social relationship is reciprocated or not, i.e. whether or not the directionality of a social link goes both ways.

The absence of a relationship (or link) is as important to the network as the presence of a relationship.

p.7
Relationship-specific structures
Some relationships structures are more fundamental than others. The presence of these structures makes the presence of other types of relationship structures more likely. In other words, some relationship structures have a profounder effect on the overall interconnectedness of a group than others. By relationship structure, we mean any axis along which people are said to be connected.

Distance-generating mechanisms
A distance-generating mechanism is any method of effecting the level of connectedness between two nodes.

Structural crystallization
The formation of strong intractable correlations among some structural relationships. This may lead to structural contradiction if the crystallization of some relationships in the network also leads to the suppression of other structural relationships. The persistent strength of some relationships may mean the perpetual weakness of others.

p.9
Models of Integration

A perfect market is an economist’s ideal of the wants and needs of individuals integrating to achieve an equilibrium price and level of production and consumption of goods. The view of the market is of individual atoms interacting to form the aggregate collective behavior.

p.10
The concept of social choice is similar to the perfect market idea. The differences are:
1) component actors are more intentional in their desire to influence the collective
2) component actors have greater or lesser amounts of influence – not all are equal in their ability to influence the collective.
3) groups of component actors may act in concert to influence the collective – they are not always acting as self-interested individuals.

Coercive and administered models break society into two groups – the elite, and the people. Some groups of individuals make decisions for the collective. These models try to minimize the influence of the average individual actor. For an extreme example, fascism.

Social choice offers the widest variety of combinations of elite and collective behavior.

p.19
Relationships among nodes can be either self-reported or empirically observed. These techniques are liable to produce different results.

p.20
When grouping a collection of individuals into a single node on a network (in order to talk about higher-order properties), relationships between these sub-groups can be deduced from the relationships between the individuals within the sub-groups.

Network Analysis attempts to explain he behavior of nodes and of the whole system by appealing to specific features of interconnectedness among nodes. The more-connected nodes are more influential to the whole system than nodes with fewer connections.

p.21
Graph Theory is the mathematical study of network behavior resulting from its interconnectedness. Mostly analyzes one type of relationship at a time.

p.22
Blockmodeling blocks groups of nodes based on structural equivalence. This de-emphasizes interconnectedness compared to graph theory. Also, unlike graph theory, it encourages views of multiple types of relationships in one analysis.

Data Reduction Problems
Given the abundance of data, there are two general strategies for representing the data simply.

Cluster analysis forms sets of nodes by clustering them together.

Multidimensional analysis uses spactial solutions. It maps interconnectedness using proximity in space, usually Euclidean space. Easier to visualize than cluster analysis.

p.23
The number of possible pairwise relationships in a network is given by:
n(n-1) for asymmetrical networks
n(n-1)/2 for symmetrical networks