
Well, exponentially greater possibilities, at least.
One of the great things about yuri (or yaoi, or, even better, bisexual characters) is that the number of possible shippings increases exponentially more with the number of characters. Let’s look at why yuri is awesome and learn a bit of graph theory while we’re at it!
First of all, how do we define a “shipping”? Generally, the term refers to a single couple: for example, I have been shipping Ringo and Shouma in Mawaru Penguindrum. However, people can ship multiple couples in a single show: for our purposes, we’ll refer to this set of pairings as a single shipping. To simplify things, we’ll assume that every character is matched to a single partner. So no threesomes or harem end.
Love Graphs
To count how many possible pairings a show has, we’re going to construct a “love graph.” Let’s start with the basics: what is a graph? The graph G = (V, E) is a set of vertices V and a set of edges E. An edge links two vertices in the graph. So in the love graph, each character is a vertex, and edges represent possible romantic links. So (a subgraph of) the love graph for Kimikiss would look like this:

We have the love triangle surrounding Kazuki, Kouichi’s love triangle, and Eiji as Kouichi’s rival for Mai. Note that the graph is bipartite: we can divide the vertices into two sets, such that all edges in the graph cross from one set to the other, simply by picking a set of boys and a set of girls. The pairings in Kimikiss are all straight.
The number of possible shippings, then, is the number of matchings on the love graph. A matching is simply a set of edges which share no common vertex— a set of couples where nobody is two-timing.
Of course, the pairings shown on the above graph are only the ones that the show itself encourages. What if we think that Sakino and Sanada make the perfect couple? Nothing wrong with that (except that Sanada is an asshole for choosing Mai and deserves to die alone and unloved). So the graph we would consider for Kimikiss in counting the number of possible shippings has edges between every pair of characters of the opposite sex. If we permit bisexual pairings, then the love graph becomes complete: there is an edge from every character to every other character in the graph.
Harems

Your typical harem has a single male character of consequence, and n females who are interested in him. How would this love graph look?
It would also be bipartite: the male character is linked to every female character, and there are no links between the female characters. If the graph has n females, then, the love graph has n possible matchings, and there are n possible shippings. Note that no perfect matching exists in the harem love graph: n-1 females must die alone and unloved. This is their lot, and we shall shed no tears for them.
Heterosexual Romance
Now let’s consider shows like Kimikiss and ef, where we have a similar number of males and females. Assume there are n characters, with an equal number of males and females. In this case, a perfect matching exists: to simplify things, we’ll count only the number of perfect matchings, where every character is part of a couple. Once again, the love graph is bipartite, with two fully interconnected vertex sets of size
. There are
such pairings. (To see this, we have
females to match the first male to,
females to match the second male to, etc. )
Yuri / Yaoi / Bisexual
Next, consider a yuri / yaoi / bisexual show such as Yuruyuri or Simoun, with a cast of n characters, any two of which are a potential item. Now our love graph is complete: every character can form a couple with every other character. Once again, we’ll count the number of perfect matchings. Assuming n is even (which it must be for a perfect matching to exist) we can determine that the number of perfect matchings is
using a similar argument to last time.
Conclusions
To summarize:

So, the number of characters being equal, a show where the genders are evenly distributed has
times as many perfect (well, for one gender) matchings as a standard harem . And yuri shows have
times as many possible perfect matchings as a heterosexual show.
So there we have it. Yuri is awesome, a realm of exponentially greater possibilities. Q.E.D.
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