The Space Syntax integration measure is technically analogous to the "gravity" and "closeness" indices in network studies. However, SSX uses a dual graph representation, where street segments (or axial lines in the case of SSX) are represented as nodes and intersections as edges. There is thus no metric distance in this representation -- proximity is instead measured in "steps" or the number of turns it takes to get from a particular axial line to another axial line. If they intersect with each other, then it is one step. If they are parallel and connected by a third line, then it is two steps etc.
Gravity and Closeness metrics offered in the UNA toolbox can measure similar qualities. If you are interested in doing simply a network level integration analysis, then you could proceed as follows. 1) select just network junctions (intersections) as your origins/destinations. 2) make sure your network has a "turns" impedance attribute. 3) run the Closeness analysis using "Turns" as the impedance attribute and a search radius that is large enough to reach the most remote parts of your network. If you want to translate the results to segments instead of nodes, perform a spatial join from nodes to segments and assign each segment the average result of its two end nodes.
To run a Closeness analysis for buildings instead, just use buildings as inputs instead of street junctions. Pls see the Help file for more details.
Andres