Collusion set detection using graph clustering

Many mal-practices in stock market trading—e.g., circular trading and price manipulation—use the modus operandi of collusion. Informally, a set of traders is a candidate collusion set when they have “heavy trading” among themselves, as compared to their trading with others. We formalize the problem of detection of collusion sets, if any, in the given trading database. We show that naïve approaches are inefficient for real-life situations. We adapt and apply two well-known graph clustering algorithms for this problem. We also propose a new graph clustering algorithm, specifically tailored for detecting collusion sets. A novel feature of our approach is the use of Dempster–Schafer theory of evidence to combine the candidate collusion sets detected by individual algorithms. Treating individual experiments as evidence, this approach allows us to quantify the confidence (or belief) in the candidate collusion sets. We present detailed simulation experiments to demonstrate effectiveness of the proposed algorithms.     

Robustness of solutions to critical node detection problems with imperfect data: a computational study

A class of critical node detection problems based upon the metric of communication efficiency is considered. While both exact integer programming and heuristic centrality-based methods exist for the solution of these problems, previous work has been mostly focused on the case where perfect information about the network is available. In this paper we suppose that some level of misinformation about nodes or edges has been inflicted on the observer's perception of the network, that is, there are hidden elements or fake additional elements. An extensive computational study is conducted to ascertain whether the exact integer-programming-based solutions perform better under imperfect information than heuristic methods. For large networks, exact methods cannot produce a solution in a reasonable amount of time, hence an approximation of the exact method is also considered for such instances. The obtained approximate solutions are again compared to centrality-based heuristics under the presence of imperfect data.