Graph Algorithm to Find Core Periphery Structures using Mutual K-nearest Neighbors

Core periphery structures exist naturally in many complex networks in the real-world like social, economic, biological and metabolic networks. Most of the existing research efforts focus on the identification of a meso scale structure called community structure. Core periphery structures are another equally important meso scale property in a graph that can help to gain deeper insights about the relationships between different nodes. In this paper, we provide a definition of core periphery structures suitable for weighted graphs. We further score and categorize these relationships into different types based upon the density difference between the core and periphery nodes. Next, we propose an algorithm called CP-MKNN (Core Periphery-Mutual K Nearest Neighbors) to extract core periphery structures from weighted graphs using a heuristic node affinity measure called Mutual K-nearest neighbors (MKNN). Using synthetic and real-world social and biological networks, we illustrate the effectiveness of developed core periphery structures.

Enhanced Affinity for Spectral Clustering using Topological Node Features (TNFS)

Data clustering is an active topic of research as it has applications in various fields such as biology, management, statistics, pattern recognition, etc. Spectral Clustering (SC) has gained popularity in recent times due to its ability to handle complex data and ease of implementation. A crucial step in spectral clustering is the construction of the affinity matrix, which is based on a pairwise similarity measure. The varied characteristics of datasets affect the performance of a spectral clustering technique. In this paper, we have proposed an affinity measure based on Topological Node Features (TNFs) viz., Clustering Coefficient (CC) and Summation index (SI) to define the notion of density and local structure. It has been shown that these features improve the performance of SC in clustering the data. The experiments were conducted on synthetic datasets, UCI datasets, and the MNIST handwritten datasets. The results show that the proposed affinity metric outperforms several recent spectral clustering methods in terms of accuracy.