Talk:Network probability matrix

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It is obvious that this was copied and pasted by a process that lost some mathematical formulas and lost the year after "Carley". But Google finds nothing on the web that matches this. Two users, NYNetwork and Smoke73, seem to have worked on several closely connected pages for a while in the spring of 2008, and have since disappeared and left not email contact (where it would say "email this user"). Michael Hardy (talk) 16:50, 17 April 2009 (UTC)

Here's the material that appears damaged. I moved it to talk since it isn't much good as is:

The edge probabilities can be derived from empirical data in several ways. Given network data collected over multiple time periods on a group of subjects, the edge probabilities can be estimated by the proportion of edge occurrences, eij, for each cell in the adjacency matrix, . In the case of communication networks, statistical distributions can be fitted to the time between messages for each potential edge in the network. For a specified period of time t, the edge probability p for each set of entities i and j can be found. Under certain assumptions, the following is true:

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In practice, the function must be estimated using techniques such as maximum likelihood estimation; it is the probability density function for the time between communications from node vi to vj, and represent the parameters of the density. It may be desirable to construct a network based on a restriction such as, “two emails within a time period demonstrate a relationship, but one does not.” In this case, it is necessary to compose a function of random variables. If [?] represents the probability density function of time between two sets of two emails and [?] represents the probability density function of time between one set of two emails, then the following is true under certain assumptions:

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It is possible to generalize this idea; if the probability that x or more communications occur within time t, then the following is true:

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This newly proposed framework for viewing the probability space of a social network preserves the same flexibility for modeling dyadic relationships, however, it provides researchers with a means to understand the probability space of the network and thus devise more robust and appropriate statistical tests for social network analysis.