Anarchism (particularly in the U.S.) is a fascinating topic to me, since it seems that it was a very frightening and powerful counterculture in its time but it is essentially never taught about in U.S. high schools or referenced in present day. President McKinley was shot and killed by a self-professed Anarchist, as were several heads of state in Europe, so it was clearly an important movement that had important historical impact.
As a movement, how tightly organized was it? Terrorism in present day is often described as a network of "cells" which function autonomously but are technically still linked or are supposedly following a leader's orders; were anarchist movements connected among nations of Europe and the U.S.? How was this movement ultimately suppressed and defeated?
I can't really speak to the organizational structure of anarchists, but I can comment a bit on anarchists and their reputation for violence. Frequently, anarchists were rounded up as "the usual suspects" when violent crime was committed, mainly because they were an easy target for politicians and police. For example, after the Haymarket was bombed in 1886, Chicago police rounded up 8 anarchists, two of whom local papers had specifically named as causes of any future trouble. The big problem? None of the 8 men committed the crime. In fact, they were charged with inciting violence (they didn't, according to the mayor of the city who was present at their rally) and conspiracy to commit the murders of policemen who were killed by the bombing (most policemen in the incident were injured or killed by friendly fire). 8 were convicted, 4 hanged, one committed suicide, 3 more were later pardoned by the governor. It's thought that the bomb thrower was an agent provocetur hired by local businessmen.
The problem is, we have no real record of when anarchists were actually behind violence and when they were convenient scapegoats for local authorities. Saccho and Vanzetti are another good example of men who came under suspicion of a crime because of their political leanings. We will mostly likely never know how many crimes we're actually committed by anarchists.
This isn't to say that anarchists didn't embrace violence as a means of achieving political goals, but that many of them didn't engage in the violence of their movement.