In the above illustration I used the well know two-dimensional political compass to locate the different political ideologies here, with one axis for left-right and the other one for how authoritarian or libertarian each ideology is. There is no way to measure how much each ideology is represented on the ground, since we never had a true elections for decades, so the size of each on the graph is somehow meant to illustrate how significant it is, without it being to an accurate scale. Also notice that I am focusing here on ideologies rather than political parties, as currently the political parties we have don't really represent all the ideologies in the streets.
Ikwan (Muslim Brotherhood): It's one of the oldest Islamist groups in Egypt and in the Arab world. It was founded in 1928, and since then it was never an official political party however it acted as a political party with its members running in the parliamentary election under the group's name. As we will see later, they are not as authoritarian as the Salafists, but the internal structure of the group and their views in the early days of January 25 revolution where the group officials opted a political struggle in the parliament rather than participating in demonstrations against the regime; all this makes me put them higher in the Authoritarian-Libertarian axis. They believe in democracy, which is one of the things that separates them from many Salafys, however they agree with them in their views that Islamic Rules (Sharia) should have higher precedence over the majority rule and personal freedom. So if the majority of the people choose something that according to their view is against religion, it shouldn't be passed. Just like many Islamic groups, their views regarding private property and ideas such as maximum wages put them to the right of the economical axis.
Their existence since more than 80 years all over the country, and the religious and social services they offer to people give them strong reach to voters in elections. They participated in the revolution a bit late, but no one can deny their effective participation in it, however the authoritarian part in their DNA came to live again right after Mubarak stepped down, they are against the continues demonstrations and sit-ins the more libertarian parties participate in nowadays, they prefer to give the Supreme Council of Armed Forces (SCAF) chance to deliver democracy to the people as they promised, which makes some say that they decide to side with SCAF (the current regime).
Salafists: This is not really a homogeneous political ideology. Salafism - sometimes referred to as Wahabism - is mainly a religious ideology, or more precisely an umbrella of ideologies, and is composed of many sub-groups and sects. There are no statistics to measure the actual number of Salafys, however it is clear that their number is big. Most of them are against opposing or revolting against the regime, even when it is an unjust one. And this was clear when many Salafists opposed the revolution during and after it, whether in Egypt or in other Islamic countries like Saudi Arabia. They are even more radical than the Ikhwan when it comes to Sharia Rules vs. the Majority Rule, and that's why some Salafists used to believe that democracy is against religion, however now after the revolution more than one Salafy parties are being formed (for example Al-Nour Party), they are having presidential candidates (for example Hazem Salah Abou-Ismail), and they are starting to participate in the political process.
Salafists have their own satellite channels, they also exist in mosques - especially in rural areas - and that's why their effect on voters is not to be neglected at all. They sure share the same point of view with the Ikhwan when it comes to opposing the current sit-ins and demonstrations taking place in Egypt.
Jihadists: This was one of the trickiest ideologies to be places on the map, on one hand they fall under the Salafy umbrella, however they are different when it comes to opposing the regime, as they believe in armed struggle against unjust regimes that do not follow the Islamic Shariaa. Al-Quaida is considered a part of the Jihadist movements by the way.
Leftists: Let's now sail to the opposite part of the map. There are sure many sub-ideologies here, but I will focus more on the common or more obvious characteristics to me. Also please notice that I am using the leftists terminology here where the leftist-liberals are just called leftists, while right-liberals are called liberals. Most of the leftists and liberals believe that the revolutions is far from over, and during the recent sit-in it was them who were there. The leftists nowadays are the ones who fight for workers rights the most, they consider demands such as minimum and maximum wages as core-demands of the revolution, and that's why the see the revolution is far from over, while for most of the parties who are located on the right part of the graph, they believe such demands are marginal demands and can be achieved later on. The leftists disagree with those parties in the upper-right quadrant of the graph on the definition of martyrs (people who died in the revolution), Some Islamists for example are against calling anybody a martyr unless he was fighting in a religious war, some others such as Folool and Couch-Party members try to differentiate between those who were peacefully protesting and those who were attacking police stations. Hence it's the leftist who are the ones who care the most about the martyrs, helping their families to get their rights back, and all those responsible for their death to be punished.
The leftists do not have any significant traditional media outlets, however they are more active online. They also should be focusing on syndicates, workers unions, and on the votes of workers and martyrs families in the coming elections, however most of the young leftists and activists are not members of any political parties.
Liberals: The main reasons for the liberals to participate in the revolution are human rights and freedom, which were murdered during Mubarak's regime. And when it comes to economical reasons, they see the problem with Mubarak regime as it was a corrupted one, and not as a capitalist one as the leftists like to say. They cannot side with the Army or accept the idea of giving them a chance to deliver democracy to people as some Islamist say, as long as they see civilians being tried in military trials and protests being crack down.
The liberals have satellite channels to reflect their opinions, but their main two problems:
Some former regime members (folool) and business tycoons try to masquerade as liberals, and speak in their names. That's why some so called elites, are considered to be representatives of the liberal stream, and they call for stuff that may repel the people away from them. Most of the time those anti-democratic - sometimes even anti-liberal - demands they make are made because they are afraid of other majorities on the ground, especially the Islamists.
The other problem is that almost all of their demands are too ideological to attract real voters compared to stuff like minimum wages or applying Islamic shariaa.
The Couch Party: This is not a real party, but a metaphor used here to refer to people who are not much into politics, and prefer to watch demonstrations from their couches instead of participating in them. They are sometimes called the silent majority as well. For me they form a huge bulk of the voters in any upcoming elections, and all other political forces should be doing their best then to affect and acquire their votes.
Folool: Those are the ex-members of Mubarak's regime, as well as those who still like him. Their numbers are not big, however many of them still occupy key positions in the regime, even SCAF is hard not to be seen as part of them. All revolutionary forces whether they are Ikhwan, Leftists or Liberals are trying their best to remove the folool from their positions and to neutralize those of them who have the ability to buy votes in the coming elections.
Disclaimer: I consider myself a liberal, so my views above might be from a liberal point of view.
I received comments from both Tarik Salama and Cerium, they both believe that Couch Party should be placed a bit on the right as they are far from being centrists, Tarik believes folool should be placed further to the right as well and Cerium believes that the Salafists size is a bit less than they are illustrated here.
In fact, as I mentioned earlier, the sizes of the parties on the graph are not to scale, as I do not have any accurate statistics, they just reflect how significant I see them in the street.
And regarding the Counch and Salafies, those are the most non-homogeneous groups, so placing them on the map, and deciding their sizes on it was a bit tricky. It's all subject to how you see each of them, and the different ideologies you see they include under their umbrellas. They both may even intersect with neighbouring groups on the graph. For example there are Ikwanis who are affected by Salafy ideologies, or Couchians who do love or at least sympathize with Mubarak!
Anyway, all this is open to discussion, and for sure the further elections might help us create more accurate graphs.
Back to the bipolar views, I've notices from the discussion on twitter that there is a trick here when it comes to how Leftists and Liberals see each other. Many leftists for example see the map from a vertical point of view, hence they believe they are closer to liberals against the authoritarian parties, while some hardcore leftists on the other hand see the graph from the horizontal view and for them it's all about the economical ideologies and this is what matters the most. I myself prefer the vertical view.
If you are looking for a list of current parties and their position in the political spectrum, I recommend this interactive graph in The Atlantic website, also there is this Political Parties Map made by Arabist.