# Finding cliques and communities with tna

The `tna` package includes functionalities for finding cliques of the transition network as well as discovering communities. We begin by loading the package and the example data set `group_regulation`.

    library("tna")
    data("group_regulation", package = "tna")

We fit a TNA model to the data.

    tna_model <- tna(group_regulation)
    print(tna_model)
    #> State Labels :
    #>
    #>    adapt, cohesion, consensus, coregulate, discuss, emotion, monitor, plan, synthesis
    #>
    #> Transition Probability Matrix :
    #>
    #>                   adapt   cohesion  consensus coregulate    discuss    emotion
    #> adapt      0.0000000000 0.27308448 0.47740668 0.02161100 0.05893910 0.11984283
    #> cohesion   0.0029498525 0.02713864 0.49793510 0.11917404 0.05958702 0.11563422
    #> consensus  0.0047400853 0.01485227 0.08200348 0.18770738 0.18802338 0.07268131
    #> coregulate 0.0162436548 0.03604061 0.13451777 0.02335025 0.27360406 0.17208122
    #> discuss    0.0713743356 0.04758289 0.32118451 0.08428246 0.19488737 0.10579600
    #> emotion    0.0024673951 0.32534367 0.32040888 0.03419105 0.10186817 0.07684173
    #> monitor    0.0111653873 0.05582694 0.15910677 0.05792045 0.37543615 0.09071877
    #> plan       0.0009745006 0.02517460 0.29040117 0.01721618 0.06789021 0.14682475
    #> synthesis  0.2346625767 0.03374233 0.46625767 0.04447853 0.06288344 0.07055215
    #>               monitor       plan   synthesis
    #> adapt      0.03339882 0.01571709 0.000000000
    #> cohesion   0.03303835 0.14100295 0.003539823
    #> consensus  0.04661084 0.39579712 0.007584137
    #> coregulate 0.08629442 0.23908629 0.018781726
    #> discuss    0.02227284 0.01164262 0.140976968
    #> emotion    0.03630596 0.09975326 0.002819880
    #> monitor    0.01814375 0.21563154 0.016050244
    #> plan       0.07552379 0.37420822 0.001786584
    #> synthesis  0.01226994 0.07515337 0.000000000
    #>
    #> Initial Probabilities :
    #>
    #>      adapt   cohesion  consensus coregulate    discuss    emotion    monitor
    #>     0.0115     0.0605     0.2140     0.0190     0.1755     0.1515     0.1440
    #>       plan  synthesis
    #>     0.2045     0.0195
    plot(tna_model)
    #> Registered S3 method overwritten by 'cograph':
    #>   method             from
    #>   plot.tna_bootstrap tna

Next, we apply several community finding algorithms to the model (see `?communities` for more details), and plot the results for the `leading_eigen` algorithm.

    cd <- communities(tna_model)
    plot(cd, method = "leading_eigen")

Cliques can be obtained with the `cliques` function. Here we look for dyads and triads by setting `size = 2` and `size = 3`, respectively. Finally, we plot the results.

    layout(matrix(1:4, ncol = 2, byrow = TRUE))
    dyads <- cliques(tna_model, size = 2, threshold = 0.2)
    triads <- cliques(tna_model, size = 3, threshold = 0.05)
    plot(dyads, ask = FALSE)
    plot(triads, ask = FALSE)