  This paper explores the spatial and temporal diffusion of political violence
in North and West Africa. It does so by endeavoring to represent the mental
landscape that lives in the back of a group leader's mind as he contemplates
strategic targeting. We assume that this representation is a combination of the
physical geography of the target environment, and the mental and physical cost
of following a seemingly random pattern of attacks. Focusing on the distance
and time between attacks and taking into consideration the transaction costs
that state boundaries impose, we wish to understand what constrains a group
leader to attack at a location other than the one that would seem to yield the
greatest overt payoff. By its very nature, the research problem defies the
collection of a full set of structural data. Instead, we leverage functional
data from the Armed Conflict Location and Event Data project (ACLED) dataset
that, inter alia, meticulously catalogues violent extremist incidents in North
and West Africa since 1997, to generate a network whose nodes are
administrative regions. These nodes are connected by edges of qualitatively
different types: undirected edges representing geographic distance, undirected
edges representing borders, and directed edges representing consecutive attacks
by the same group at the two endpoints. We analyze the resulting network using
novel spectral embedding techniques that are able to account fully for the
different types of edges. The result is a map of North and West Africa that
depicts the permeability to violence. A better understanding of how location,
time, and borders condition attacks enables planning, prepositioning, and
response.
