Graph Algorithms for Fraud Detection and Community Detection: Modularity, Louvain, Infomap, node2vec and comE

The presentation begins with a typical financial loan workflow, highlighting the need to detect fraudulent groups that can cause massive losses, and introduces graph algorithms as a way to link suspicious entities and block them collectively.

Basic graph notation G = (V, E) is defined, where V is the vertex set and E the edge set (directed/undirected, weighted/unweighted). Common centrality metrics—degree, closeness and betweenness—are described with examples of how they reveal influential nodes in a fraud network.

Community detection methods are listed, including minimum cut, non‑negative matrix factorization, modularity‑based partitioning and similarity‑based clustering. The modularity objective is explained: dense intra‑community connections versus sparse inter‑community links, with the standard formula and its simplified version illustrated.

The Louvain algorithm is detailed in two phases: (1) Modularity Optimization, where each node is moved to the neighboring community that yields the greatest modularity gain, and (2) Community Aggregation, where communities are collapsed into super‑nodes and the process repeats until modularity stabilizes.

Infomap is introduced from an information‑theoretic perspective, showing how random walks are encoded with minimal bits when community structure is strong; the map equation and the iterative process of assigning nodes to communities that reduce the average description length are outlined.

Graph embedding techniques are covered next. DeepWalk samples random walks to generate node co‑occurrence pairs and trains a skip‑gram model. node2vec extends this by biasing walks with parameters p (return) and q (in‑out) to balance breadth‑first (BFS) and depth‑first (DFS) exploration, with formulas for transition probabilities.

The comE algorithm is presented as a joint community detection and embedding method that integrates a Gaussian mixture model with graph‑based similarity, aiming to overcome the two‑stage pipeline of separate embedding and clustering.

Evaluation metrics for community quality are listed, including Modularity, Normalized Mutual Information (NMI) and Adjusted Rand Index (ARI), with brief formulas shown.

Finally, a collection of reference links to papers, tutorials, and implementations (e.g., Spark GraphX, Fast Unfolding, spectral clustering) is provided for further study.