====== Blockmodeling ======

{{http://mrvar.fdv.uni-lj.si/pub/mz/mz1.1/batagelj.pdf|Generalized blockmodeling with Pajek}}

===== Indirect approach =====

[[http://vlado.fmf.uni-lj.si/pub/networks/data/test/class.net|Class]]

We read a network in Pajek. The clustering procedure is quite time (and space) consuming for larger networks. Because of this, for clustering the network, we have first to specify the set of nodes to be clustered by providing a corresponding cluster. In our case we want to cluster a whole network
<code>
Cluster/Create complete cluster
</code>
Now we can compute a dissimilarity ([[http://mrvar.fdv.uni-lj.si/pajek/pajekman.pdf|Pajek manual]], page 51). We select the corrected Euclidean distance. The dissimilarity command automatically makes clustering and ask for the name of EPS file on which it stores the picture of a dendrogram.
<code>
Operations/Network+Cluster/Dissimilarity* [5][1][dendro.eps]
</code> 

{{ru:7iss:labs:classdend.png?300}}

Assume that from the dendrogram we decide to produce 4 clusters. To get them we click on the hierarchy register. A new window opens with a tree display of the hierarchy. We drill into the corresponding levels and close the corresponding tree nodes using ''Edit/Change Type''. 

{{ru:7iss:labs:close.png?250}}

We close the window. Now we can get the partition and, for later use, also a permutation:
<code>
Hierarchy/Make partition
Hierarchy/Make permutation
</code>
To draw a network with the obtained partiton we use
<code>
select the original network
Draw/Network+First partition
</code>

{{ru:7iss:labs:class4.png}}

We produce a matrix representation of a clustered network using 
<code>
File/Network/Export as matrix to EPS/Using Partition+Permutation
</code>

{{ru:7iss:labs:classmat.png?400}}

===== Direct approach =====

==== Class ====


[[http://vlado.fmf.uni-lj.si/pub/networks/data/test/class.net|Class]]

<code>
read class.net
Network/Create Partition/Blockmodeling*/Random start [structural equivalence, 4 clusters]
Network/Create Partition/Blockmodeling*/Random start [regular equivalence, 4 clusters]
</code>

==== Tina / LJ student government ====

{{pub:zip:tinabm.zip|BM}}

<code>
read tina.net
Network/Create Partition/Blockmodeling*/Random start [regular equivalence, 4 clusters]
Network/Create Partition/Blockmodeling*/Random start [user defined, 4 clusters]
</code>

==== Football market ====

''C:\Users\batagelj\Documents\papers\2017\Moscow\bm''

[[http://vlado.fmf.uni-lj.si/pub/networks/doc/ECPR/nets/F2002.net|F2002.net]]; {{ru:7iss:labs:football02.pdf}}


<code>
read Football.net
Network/Create new network/Transform/Line values/Set all line values to 1
Network/Create Partition/Blockmodeling*/Random start
</code>

We would like to detect a hierarchical (acyclic) structure in this network. Based on the theorem that the nodes of an acyclic network can be reorder in such a way that the corresponding matrix has a zero lower triangle we can construct a pre-specified blockmodel imposing this restriction. Using the penalty value for a block we can make some errors more important. We assumed a clustering in k=6 clusters. 

{{ru:7iss:labs:bmacy6.png?550}}

For a later use we saved the pre-specified blockmodel to the file ''acyclicDNC6.mdl''. We obtained 10 nonequivalent solutions with the criterion function value = 0. Inspecting them in Pajek we selected the following solution because it has well balanced sizes of clusters

{{ru:7iss:labs:bmfb6pic.png?550}}

We draw the corresponding matrix representation.

<code>
select partition
Partition/Make permutation
File/Network/Export as matrix to EPS/Using Partition+Permutation
</code>

{{ru:7iss:labs:bmfb6.png}}

If we assume that the data a correct (no measurement errors) we can determine the acyclic structure faster and exactly using the theorem: if we shrink each strong component of a directed graph into its own model node then the obtained blockmodel is acyclic (with loops allowed). This blockmodel has the smallest number of levels and each node is at its lowest level. Other solutions can be obtained by promoting some nodes to higher level. This procedure can be used also for very large networks.

<code>
Network/Create Partition/Components/Strong [1]
Operations/Network+Partition/Shrink Network [1][0]
Network/Create New Network/Transform/Remove/Loops [yes]
Network/Acyclic Network/Depth Partition/Acyclic
select strong components partition as First
select depth partition as Second
Partitions/Functional Composition First*Second
Partition/Make Permutation
select original network
File/Network/Export Matrix to EPS/Using Partition+Permutation
</code>

It turns out the our network has 44 nodes and 40 strong components - it is almost acyclic. It requires 6 levels (clusters). The final picture was obtained by manual transposition of some nodes inside clusters.

{{ru:7iss:labs:bmfbacyc.png}}


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