Self-Liking Group in Networks With Multi-Class Nodes

Nodes in complex networks are generally allocated into groups using community detection methods. These communities are based on the interactions between nodes (links). Conversely, in machine learning, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">clustering methods</i> group data points into classes based on their attribute's similarities regardless of their interactions. Although both communities and clustering methods classify data points into groups, they are fundamentally different. Clustering relies on attribute similarity, while communities focus on interaction patterns. The present study bridges these two distinct approaches by introducing a new concept - Self-Liking Groups (SLG). Based on entropy considerations, SLG quantifies the preference of node classes to interact with similar ones based on their communication patterns, thus combining both the community and the clustering methods. We demonstrate SLG in three case studies: (i) A career network of 2.5 million companies, linked by 8 million job switches. Here, SLG reveals the openness of different industrial sectors to workers in other sectors. For example, the Healthcare sector shows the highest SLG, i.e., it is the least open to accepting workers from other sectors, while the Energy sector has a high SLG, but only for educated workers. Also, managers' shift between different sectors is more limited due to higher SLG. (ii) A scientific co-authorship network where SLG measures the openness of collaboration between different countries. China, India and Japan, have stronger SLG and are thus more likely to collaborate with scientists in their own country compared to the USA, Canada, and most EU countries. (iii) In the medical scientific research space, SLG reveals that Japan, a country known for its longevity, is extremely close compared to China or India. We also find that SLG is a stable measure across various community detection methods and initial parameter spaces. This implies that SLG captures a fundamental property of networks with heterogeneous nodes and is useful in analyzing real complex network scenarios.