1. A computer-implemented method comprising: retrieving a social graph including a plurality of nodes and a plurality of edges, each of the nodes corresponding to a member in a social network service and each of the edges representing a connection between members of the social network service; for each node of the plurality of nodes in the social graph: creating a vertex-centric partial graph for the node, the vertex-centric partial graph identifying the node as a vertex with a specific vertex node and containing nodes from the partial graph, the nodes from the partial graph being only nodes reachable within limited hops from the node, wherein a hop is a distance of one edge between nodes; determining a list of the nodes reachable in one hop, without intermediate nodes, from the vertex; adding the list of nodes reachable in one hop to a first degree list for the partial graph; determining a list of nodes reachable in exactly two hops from the vertex, and reference counts as to how many distinct paths exist, in the social graph, between the vertex and each of the nodes reachable in exactly two hops from the vertex; and adding the list of nodes reachable in two hops and the reference counts to a second degree list for the partial graph; maintaining a global inverted index containing a list of all nodes in the social graph and for each node in the social graph a list of nodes that directly connect to the node in the social graph; distributing the partial graphs created for each of the plurality of nodes across a plurality of data servers; and distributing the global inverted index containing the list of all directly connected nodes to the data servers to facilitate a network computer breadth-first distance traversal.