Monday, July 28, 2008

Tags and SNA measures

Studies on tags commonly have the triple of {user, tag(s), item} as a unit of study. That's also what I'm interested in, especially in those underlying structures that build relationships between users, tags and items. Some apply Social Network Analysis to study, for example the centrality measures of the network.

A run-down of SNA measures from Wikipedia

Degree an individual lies between other individuals in the network; the extent to which a node is directly connected only to those other nodes that are not directly connected to each other; an intermediary; liaisons; bridges. Therefore, it's the number of people who a person is connecting indirectly through their direct links.
(Somewhere else:The betweenness measurement indicates a node or nodes that connect clusters of nodes. Nodes that have hight betweenness have high influence over what information flows in the network.)
The degree an individual is near all other individuals in a network (directly or indirectly). It reflects the ability to access information through the "grapevine" of network members. Thus, closeness is the inverse of the sum of the shortest distances between each individual and every other person in the network.
(Degree) centrality
The count of the number of ties to other actors in the network. See also degree (graph theory).
Flow betweenness centrality
The degree that a node contributes to sum of maximum flow between all pairs of nodes (not that node).
Eigenvector centrality
a measure of the importance of a node in a network. It assigns relative scores to all nodes in the network based on the principle that connections to nodes having a high score contribute more to the score of the node in question.
The difference between the n of links for each node divided by maximum possible sum of differences. A centralized network will have many of its links dispersed around one or a few nodes, while a decentralized network is one in which there is little variation between the n of links each node possesses
Clustering coefficient
A measure of the likelihood that two associates of a node are associates themselves. A higher clustering coefficient indicates a greater 'cliquishness'.
The degree to which actors are connected directly to each other by cohesive bonds. Groups are identified as ‘cliques’ if every actor is directly tied to every other actor, ‘social circles’ if there is less stringency of direct contact, which is imprecise, or as structurally cohesive blocks if precision is wanted.
(Individual-level) density
the degree a respondent's ties know one another/ proportion of ties among an individual's nominees. Network or global-level density is the proportion of ties in a network relative to the total number possible (sparse versus dense networks).
Path Length
The distances between pairs of nodes in the network. Average path-length is the average of these distances between all pairs of nodes.
Degree an individual’s network reaches out into the network and provides novel information and influence
The degree any member of a network can reach other members of the network.
Structural cohesion
The minimum number of members who, if removed from a group, would disconnect the group.[15]
Structural equivalence
Refers to the extent to which actors have a common set of linkages to other actors in the system. The actors don’t need to have any ties to each other to be structurally equivalent.
Structural hole
Static holes that can be strategically filled by connecting one or more links to link together other points. Linked to ideas of social capital: if you link to two people who are not linked you can control their communication.
What made me think of this now was that I read this mini study Using Social Network Analysis to Highlight an Emerging Online Community of Practice. Anthony Cocciolo, Hui Soo Chae, Gary Natriello, Teachers College, Columbia University

The method used made me tick. They used
..System Theory to define the uploading and downloading of materials as "communicative acts", the users of the system were the "actors" and the cululative communicative exchanges as "interactions" (Buckley, 1967). .. this particular systems arrangement is useful because it provides a readily available metric for assessing actors' interactions within a network.
I think it might be interesting to think how this could be used to study the underlying networks with tags.

The most comprehensive reference is: Wasserman, Stanley, & Faust, Katherine. (1994). Social Networks Analysis: Methods and Applications. Cambridge: Cambridge University Press. A short, clear basic summary is in Krebs, Valdis. (2000). "The Social Life of Routers." Internet Protocol Journal, 3 (December): 14-25.

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