May I suggest with the easier figure to kick things off.
Elder's graph is comparing the numbers of Arabs killed by Israelis with the number of Arabs killed by other Arabs. (There's something really creepy about looking at numbers killed by race on the one hand and nationality on the other - but let's leave that distasteful issue to one side).
We also need to establish a sense of scale as well. 'Arabs' is a nebulous description and dwarfs the numbers of Israelis - so we need to have some sense of adjusting for the differences in numbers.
I would suggest we look at the numbers who are taking part in the killing - in the Israeli section this would mean those in the IDF. Active numbers of the military is about 200,000 with about 500,000 (taking high estimates) in reserves. Arguably we should take the number who are active.
Then we come to the numbers killed. Elder has chosen 1948 - the formation of modern day Israel. That's a clear enough date - and so let's work with that.
Elder has estimated about 50,000 Arabs killed by Israel (less that the highest estimate of 60,000).
As pointed out earlier, this excludes Arabs (including Palestinians) killed in Lebanon in the 80s when the Israelis jumped into the middle of the Lebanese Civil War and bombed Lebanon and invaded the country. Estimates of the numbers they killed then (directly and indirectly) need to be added. I suggest 20,000 as a reasonable guesstimate.
Therefore I'd say my figures for Arabs killed by Israel since 1948 is 70,000 (taking Elder's estimate and adding the ones killed by Israel in Lebanon).
To give a sense of scale, I'd say we express this as a number killed per 100,000 of active military - which gives us 35 killed per 100,000 active members. (This is a crude measure - we're taking a total over 60 years and dividing it by a point estimate - a better measure would be an average of the soldiers over the 60 years, but that would give a lower figure for soldiers and a higher figure of deaths per 100k soldiers).
I'll leave others to show what the comparitive figures for the various Arab on Arab conflicts are and give their workings.
I have no idea whether the calculations will show that Arabs are more bloodthirsty per combatant than the Israelis - we need to look at the calculations. I think it is unlikely that the hundreds more killed in the civil war will be outweighed by the higher number of combatants - i.e. I would expect that Saddam's regime has indeed killed more Iraqis per 100,000 of his troops - the calculations will bear out by how much. Overall I'm not sure the picture will be any clearer - there are figures of killings in countries where the numbers killed have been relatively low (and this will bring the overall figure down).
[Edit: a quick calculation for Iraq, using 375k as the size of army in 2003 (it was 500k in the iran-iraq war) and using Elder's estimate of 700k killed, gives Saddam's era a whopping 1867 per 100k - i.e. over 50 times that of Israel.
Note that this is using Elder's figure without first examining it for credibility.
Also, interesting to note the figures when we use population size as a different measure (which may be the best we can use when we look at Algeria, for example). Roughly, Iraq is 'only' twice times as bloodthirsty as Israel using this measure - using a population of 31m for Iraq and 7m for Israel.)
I.e. per capita, for every 2 Arabs killed by Iraqis, the Israelis killed one Arab. And that is taking the numerically worst example from the list used for the graph. Not a great statistic..