A RoleSim implementation creating using networkX for processing
The theory and implementation details have been obtained from the paper - https://arxiv.org/abs/1102.3937 - Axiomatic Ranking of Network Role Similarity by Jin et al. (2011).
The RoleSim algorithm is a converging algorithm that attempts to approximately solve the NP-complete problem of role discovery within a reasonable number of iterations, within suitable computational complexity. In spite of operating this way, there is still a massive number of computations involved in creating an n * n matrix, and the process often times out.
The Iceberg RoleSim algorithm is a layer on top of the RoleSim algorithm that prunes out unimportant and unrelated nodepairs to identify nodes that seem to have the most interesting connections, thus reducing the order of magnitude of the processing to a manageable extent.
This implementation of RoleSim attempts to keep all the processing of the code within networkX, and thus still runs upon the CPU. On a graph with 5100 nodes, pruned by hyperparametric tuning to 665 nodes, the algorithm still takes approximately 11 minutes per iteration, and thus it is recommended that pruning be done to an extent that keeps the pruned graph within 500 nodes.
Hyperparameters that are available are alpha (initialization parameter), beta (decay rate), theta (pruning threshold) and delta (convergence threshold).
The input to the code must be a networkX graph, and it is recommended to not provide node and edge parameters, and to use a node_id-to-index/index-to-node_id dict format that converts the unique IDs of your graph into a number format. This aids in the final analysis, and allows smooth computation, without using too much memory.
The output of the code is a completely interconnected graph consisting of only the pruned nodes, with edge weights denoting a similarity value between the two nodes that are connected by the edge. This can be analyzed in multiple ways, and there is a basic histogram-based implementation of analysis presented as an example.
-A GPU implementation of the algorithm might help speed up computations.
-Dynamic programming and memoization are also alternatives expected to have significant benefits.
-A Numpy based processing approach was attempted, but the results were comparatively worse than through the current published implementation in NetworkX.