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Mathematics LibreTexts

4.3: Relation Properties

 

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A graph, as we discussed in the last chapter, is made up of both the actors and the relations among the actors. The relations among the actors (the line segments in a simple graph or the arrows in a directed graph) can also have "attributes." Sometimes it can be very helpful to use color and size to indicate difference of kind and amount among the relations. You can be creative with this idea to explore and display patterns in the connections among the actors in a network. Here are a few ideas of things that you could do.

Suppose that you wanted to highlight certain "types" of relations in the graph. For example, in a sociogram of friendship ties you might want to show how the patterns of ties among persons of the same sex differed from the patterns of ties among persons of different sexes. You might want to show the ties in the graph as differing in color or shape (e.g. dashed or solid line) depending on the type of relation. If you have recorded the two kinds of relations (same sex, different sex) as two relations in a multiplex graph, then you can use NetDraw'sProperties>Lines>Color from the menu. Then select Relations, and choose the color for each of the relations you want to graph (e.g. red for same-sex, blue for different-sex).

Line colors (but not line shapes) can be used to highlight links within actors of the same type or between actors of different types, or both, using NetDraw. First select Properties>Lines>Node-attribute from the menus. Then select whether you want to color the ties among actors of the same attribute type ("within") or ties among actors of different types ("between"), or both. Then use the drop-down menu to select the attribute that you want to graph.

If you have measured each tie with an ordinal or interval level variable (usually reflecting the "strength" of the tie), you can also assign colors to ties based on tie strength (Properties>Lines>Color>Tie-strength). But, when you have information on the "value" of the relations, a different method would usually be preferred.

Where the ties among actors have been measured as a value (rather than just present-absent), the magnitude of the tie can be suggested by using thicker lines to represent stronger ties, and thinner lines to represent weaker ties. Recall that sometimes ties are measured as negative-neutral-positive (recorded as -1, 0, +1), as grouped ordinal (5=very strong, 4=strong, 3= moderate, 2=weak, 1=very weak, 0=absent), full-rank order (10=strongest tie of 10, 9=second strongest tie of 10, etc.), or interval (e.g. dollars of trade flowing from Belgium to the United States in 1975).

Since the value of the tie is already recorded in the data set, it is very easy to get NetDraw to visualize it in the graph. From the menus, select Properties>Lines>Size. Then, select Tie-Strength and indicate which relation you want graphed. You can select the amount of gradation in the line widths (e.g. from 0 to 5 for a grouped ordinal variable with 6 levels; or from 5 to 10 if you want really thick lines).

Using line colors and thickness, you can highlight certain types of ties and varying strength of ties among actors in the network. This can be combined with visual highlighting of attributes of the actors to make a compelling presentation of the features of the graph that you want to emphasize. There is a lot of art to this, and you will have to play and experiment. Node and line attributes can obscure as well as reveal; they can mis-represent, as well as represent. Sometimes, they add to the confusion of an already too-complicated graph.