ANT6447: Applications of Network Models

Glossary to accompany this course and the manuscript "Network Models and their applications” (Revised 7/2001).

Anchorage:

Arc: A directed relationship, e.g. a link where a gives something to b would be graphed as an arc from a to b.

Betweenness: A variety of centrality indicating that some nodes are dependent on another in order to reach each other.

Capacity: A value associated with an arc, indicating the amount of something which can or does flow across a relation.

Catij "group": In a specialized "Catij" analysis, a "group" is composed of persons who have similar views of their relationships with others in a given closed membership universe. This may or may not result from their being members of the same clique. In general, ethnographic evidence must be relied upon to decide the meaning of factors and group membership. After the catij matrix is derived, it is factor analyzed by rows, using the varimax rotation. Persons with at least a 0.6 factor loading are chosen for inclusion in a "group."

Centrality: A condition of closeness and/or betweenness of nodes in a network. Closeness centrality implies autonomy and independence. Betweeness centrality implies power over others.

Closeness: A measure of the degree to which a node is adjacent to or can reach others in a network. Closeness is usually measured by the number of steps it takes to reach others.

Cluster: A subset of points whose subgraph is relatively dense (Barnes).

Clustering: The tendency to form subsets of relatively dense nodes in a network.

Cohesion: The condition of adjacency. The number of reciprocated choices. (Fernyer)

Communication pathways: Paths between nodes across which communication can take place.

Comprehensive Planning: (Also called "community planning "community organization") "A process by which a communit identifies its needs or objectives, establishes prioriti among them, finds resources for dealing with them, takes action with respect to them, and in so doing extends and develops cooperative and collective attitudes and practi in the community" (Ross cited in Dunham, 1985, p.27).

Connectedness: The rate at which all the potential links in a network are in fact connected. A measure of connectedness of a set of points N among which there are L links is the ratio of L/N(N-1). (see density)

Cut point: Point whose removal results in a disconnected graph.

Degrees: The number of lines that come out of or go into point.

Density: Density is similar to connectedness but tends to be used when one is viewing the phenomenon from the outside. Network density can be used to show solidarity or interaction (eg. establishing tribal status for a Native American community).

Distance: Distance is the length of the shortest path joining two points (Harary). Geodesic distance is the path of minimum length; the length of a geodesic is the distance from one point to another. If a second point cannot be reached from the first, the distance from the first to the second is said to be infinite (Barnes).

Equivalence structures: Structures of nodes that have similar positions in a network even if they dot no have direct relations with one another.

Flow: The movement of something across a relation or set of relations among nodes. The rate of flow is usually measured by capacity.

Formal hierarchical system: "A complex system in which some of the subsystems are subordinate to the wider system or subsystem within which it lies. More exactly, in a hierarchical formal organization each system consists of a 'boss' and set of subordinate systems" (Simon 1977 p.196‑197).

Geodesic distance: The path of minimum length; the length of a geodesic is the distance from one point to another. If a second point cannot be reached from the first, the distance from the first to the second is said to be infinite (Barnes). The shortest path.

Graph: a diagram consisting of nodes and links and representing logical relationships or sequences of events.

Hierarchy or Hierarchic systems: "All complex systems are analyzable into successive sets of subsystems" (Simon 1977 p.197).

Hierarchical levels: "In ordinary usage we tend to reserve the word 'hierarchy' for a system that is divided into a small or moderate number of subsystems, each of which may be further subdivided ... a hierarchical system is flat at a given level if it has a wide span at that level" (Simon p.198‑199). "In hierarchies we can distinguish between the interactions among systems, on the one hand, and the interaction within the system ‑‑that is, among the parts of those subsystems -- on the other. The interactions at different level may be, and often will be, of different orders of magnitude (Simon 1977 p.209).

Hierarchy of a system: (eg a city, state and nation, autonomous and yet dependent on a higher level) (see lev of integration)

Integration index: indicates how far beyond chance is the tendency for a portion of a network able to establish linkage outside of its own cluster rather than only with each cluster.

Isomorphic: Having a one to one correspondence (Yamagishi 1990 p.154). Two digraphs are said to be isomorphic if there exists a one‑to‑one correspondence between their points which preserve their directed lines.

Levels of integration: Recognition of the relative inclusiveness of subsystems within a hierarchically organized system of relations. A subsystem of relatively wide, relatively inclusive span, is said to be at a higher level of integration than a subsystem of narrow span.

Linkage: A relationship between two elements in a network system. "The provision or exchange of a specific service or material resource by one agency with another. It can be unidirectional or bidirectional" (Loeb 1991 p.6).

Matrix: A set of numbers or terms arranged in rows or columns.

Multidimensional relationship: "Multidimensionality allows for individual differences in the importance of activities to subjects" (Barton in Gottlieb 1982 p.157).

Multiplex relationships: "...Multiplexity measures only whether relationships involve two or more activities" (Barton in Gottlieb 1982 p.157).

Network: System of interconnected nodes.

Orbit: "... each equivalence class is called an orbit on graph" (Everett 1985, p.355).

Point bases: A minimal set of points of a graph D which are reachable from all points of D. (eg a communication base is the minimal collection of people required for a message to reach everyone, or the collection of people who will learn of a message originated in the network.

Queuing point: a node in a flow network where flow is impeded by restricted capacity along one or more arcs emanating from that point.

Range: The number of direct links from ego to other node the range of ego.

Reachability: a point v is reachable from point u if there exists a path from u to v.

Regular Equivalence: All the organizations that have direct or indirect relations to equivalent organizations are said to be regularly equivalent. "Regular equivalence yields groupings of points in which for every pair of persons (points, organizations etc.) the equivalent position, if one has a relation with a person (point, organization, etc.) in the second position, to other has an identical relation with a counterpart in that position" (White 1983, p.214).

Scale: A system of classifying in a series according to a standard of relative size, amount, rank, etc. (see correspondence analysis, multidimensional scaling, etc.).

Segregation index: indicates how far beyond chance is the tendency for two sets of points of a network to be isolated from one another.

Span: The span of a set is the number of links to ego (L plus the number of links among nodes which are linked to (Lne) divided by the total number of links in the set (L The measure of span is (Le+Lne)/Lt.

Structural equivalence: "... organizations that might be said to have similar positions in the network, even if they do not have direct relations with one another. Such organizations are said to have structural equivalence" (Wolfe 1985, p.25). Structural equivalence yields groupings of points which, whether or not they relate to each other, relate to other points in similar ways; "network blockmodeling under this equivalence preserves the semigroup of relations on the network, but is too restrictive to capture the more abstract basis of role parallels" (White 1983, p.213". "...if two vertices a, b of graph G are structurally equivalent then interchanging a and b would not change the overall graph (Everett 1985, p.354).

Transaction: A transaction is an event which happens across a link through time. A transaction can be unidirectional.

Transitivity: The transitivity closure of a given digraph is the minimal transitive digraph containing D.

Uniplex: Contrasted with multiplex, uniplex links have only one kind of content in the relationship. Multiplex links are those with more than one kind of content.

Urban metropolitan area: "The general concept of a metropolitan area is one of a large population nucleus, together with adjacent communities which have a high deg of social interaction with the nucleus...[It includes] a central counties the counties within which the central c is located and adjacent counties with at least 50 percen their population within the urbanized area" (Statistical Abstract of the United States 1983, p.895).

Urban metropolitan system: The system of all human servi within an urban metropolitan area, including subsystems.