Testing Goodness of Fit of Random Graph Models

Abstract

Random graphs are matrices with independent 0-1 elements with probabilities determined by a small number of parameters. One of the oldest models is the Rasch model where the odds are ratios of positive numbers scaling the rows and columns. Later Persi Diaconis with his coworkers rediscovered the model for symmetric matrices and called the model beta. Here we give goodness-of-fit tests for the model and extend the model to a version of the block model introduced by Holland, Laskey and Leinhard.

Development and investigation of methods of graphic-functional modeling of distributed systems

“…As noted above, all of the graph-analytic models of distributed systems, presented, in particular, in the papers [15][16][17][18][19][20][21][22], reproduce the static properties of the modeled objects. The object dynamic properties are characterized by separate models, which are integrated with the static component at the interface between the application software and the configuration files.…”

“…This issue is especially relevant to the microprocessor control systems for railway automatics, mainly for the points and signals interlocking. The technological object of such systems is the track development of railway stations, the research of graph-analytical reproduction of which is done in the papers [15][16][17][18][19][20][21][22].…”

“…The issues of improving the interpretation of the matrix of geometric models based on random graphs are considered in the paper [19]. Similarly to the paper [15], the block representation of the topological matrix of a continuous graph is proposed.…”

“…Either way, it is necessary to generalize the methods, models and means of graph-analytical modeling of distributed technological systems and objects, set forth in the writings [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In the aspect of the application of these categories in order to research the work and automated design of information management systems, one can distinguish such general limitations and disadvantages:…”

Estimating Parameters of a Probabilistic Heterogeneous Block Model via the EM Algorithm

“…By the model, this affinities are added together on the level of the log-odds. This so-called k-β model, introduced in [48], is applicable to social networks, where attitudes of individuals in the same social group (say, u) are the same toward members of another social group (say, v), though, this attitude also depends on the individual in group u. The model may also be applied to biological networks, where the clusters consist, for example, of different functioning synopses or other units of the brain, see [49].…”