Network analyses via matrix algebra commands

Post date: Jun 23, 2013 10:58:54 PM

The matrix algebra facility in UCINET is probably better thought of as a command-line interface. It is especially useful because you can enter the commands in a text file and then run them automatically (see this page on the batch capability). Here are some of the commands that are available, focusing on the more "networky" capabilities.

In this documentation, we often use the standard dataset "campnet" as an example. It is a directed graph. We also use campsym, which is just an undirected version, calculated by typing

-->campsym = symmet(campnet)

Centrality (and related) Measures

These are routines where the output is a value for each node.

Beta Centrality. Calculates Bonacich's (1987) power measure.

-->liked = transpose(campnet)

-->liked-beta = betacent(liked) // value of beta is automatically set to 0.995/max eigenvalue

-->liked-b05 = betacent(liked 0.5) // user chooses the value of beta to be 0.5

-->liked-betacent = betacent(liked 0 auto 0.05) // centrality is calculated for many values of beta: 0, 0.05, 0.10, 0.15 .... 0.995/maxeigen

Betweenness. Calculates Freeman's betweenness centrality.

-->campnet-bet = betweenness(campnet)

Degree. Calculates indegree and outdegree (or just degree in the case of undirected graphs).

-->campnet-deg = degree(campnet)

Centrality. Calculates a variety of centrality measures.

-->campnet-cent = centrality(campnet)

Egonet Density. Calculates the density of each node's ego network. Same as a node-level clustering coefficient.

-->campnet-egoden = egodensity(campnet)

Detecting Subgroups/Clusters

These procedures either produce a partition of nodes into groups, expressed as a categorical vector, or an actor-by-cluster membership matrix.

Cliques. Identifies all of cliques of a given size or greater and saves an actor-by-clique indicator matrix.

-->campsym = symmetrize(campnet)

-->camp-cliq = cliques(campsym 3) // output only cliques of size 3 or greater

n-Cliques. Identifies all of n-cliques of a given size or greater and saves an actor-by-clique indicator matrix. You must choose the value of n.

-->camp-cliq = ncliques(campsym 2 3) // outputs all 2-cliques of size 3 or greater

k-Core Level. Finds the k of the highest level k-core that a node participates in

-->camp-klev= kcorelev(campsym 2 3) // outputs all 2-cliques of size 3 or greater

Newman Community Detection. Partitions nodes into k classes so as to maximize Q modularity statistic using Newman's agglomeration method.

-->camp-ncd = ncd(campsym 3) // here the 3 indicates that you want a 3-cluster partition

Factions. Partitions nodes into k classes so as to maximize Q modularity statistic using a tabu search combinatorial optimization method. Not suitable for large datasets.

-->camp-fac = factions(campnet 3) // here the 3 indicates that you want a 3-cluster partition

Factions. Partitions nodes into k classes so as to maximize Q modularity statistic using a tabu search combinatorial optimization method. Not suitable for large datasets.

-->camp-fac = factions(campnet 3) // here the 3 indicates that you want a 3-cluster partition

Miscellaneous Measures

Density. Computes the density of input networks.

-->camp-den = density(campnet)

-->samp-den = density(sampson)

Geodesic distances. Computes the geodesic distance between all pairs of nodes. By default, undefined distances are assigned missing values.

-->camp-geo = geo(campnet)