Component analysis is the underside of looking at paths in a network. There will be circumstances in which a dataset is not connected and two or more separate clusters appear in a network diagram (as well as individual isolates). There can be no paths (geodesic or otherwise) between these separated clusters (components). In this situation SNA talks of there being two (or more) separate components. (Note also that an isolated node will count as a component.)
Personally, I tend avoid the term component and refer to network fragments or clusters. A component is something that is shaped, fitted and functionally integrated to a larger system. The procedures in SNA find distinct separated fragments rather than components in a functional sense. I see SNA component analysis as dealing with baseline connectivity (connection or no connection).
NetDraw’s [and UCINET] Analysis ->Components procedure checks for this baseline connectivity. Both the Friendship and Advice networks are fully connected. All nodes are in one component.
A refinement of component analysis looks at potential separations. It seeks out single nodes or lines which, if taken away, break up a network. The term for a node with this property is ‘cutpoint’ (i.e. point and node are synonyms). The clusters that remain components (cf. large, central component in random graphs). If the cutpoint is included as a member of both compenents it connects they are blocks’, hence the NetDraw label: Analysis -> Cutpoints and blocks).
Using NetDraw’s Analysis -> ‘Cutpoints and blocks’ procedure the Krack-Sociom Advice and Friendship networks do not have any cutpoints. Not only are all nodes in one component but there are no cutpoints whose deletion will break up the network. (Some textbooks talk of ‘cut ties’, however the nodes each end of cut tie will be cutpoints.)
The Zachary karate club data does have a cutpoint which NetDraw’s analysis locates. Open this dataset in NetDraw. If you run Analysis ->Components you find all nodes are in the one component. However, run Analysis ->Cutpoints and blocks.
The node ‘1’ is a cutpoint. Without it the cluster to right, and the ‘pendant’ (12) would be disconnected.
The results are stored as new node data and are available in the drop-down list in the Nodes tab.
- Drop-down chevron in the Nodes tab.
- Select a block to get members and non-members
- The three blocks are: Block 1: node 1 and the cluster to its right, Block 2: node 1 and all other nodes except 12, Block 3: note 1 and node 12.
You can also access the block membership lists in the Node attribute editor.
One very important use for Analysis ->Components is to sort out a very large dataset. Open NetDraw and load the TASA thematic groups – Interpersonal dataset. (This takes a minute or so.) You will get an big blob! It is valued data (like the Zachary dataset), so use the tie filter for >2 and then hit the layout button. (If the layout does not work as expected just hit it again.)
The layout procedure shows there is one major component and many smaller ones. Run Analysis ->Components and look in the Node tab drop-down list for Component sizes.
We now have the details;
The large, central component has 264 nodes. The next largest (purple colored to the left) has only 17. The components of size 1 are the isolates (black squares on the left) components of size 2, 3 and 4 are scattered through the crescent around the central component.
The display gives the array of components, by size. You can now investigate any component. You may decide to only retain only the large component for analysis. (These are questions of judgement.)
A note on weak components
The Zachary karate data and the TASA thematic groups are both bi-directional (undirected) data. Directed data (di-ties), as with the Krack-Sociom datasets, produce the possibility that a node is connected in one direction only. SNA defines this as creating a weak component. However, it will be a separate component if the algorithm is set to detect strong components only.
The UCINET Multiple Cohesion measures is set to a strong component default (although NetDraw Analysis is set to the weak component). Thus the multiple cohesion output for the Friendship network (where Gra-7 and Ian-9 have no outgoing ties) tells us this network has 3 components and Connectedness and Fragmentation scores (Connectedness is 19/21 =0.905 and Fragmentation is 1-.905 = 0.095)