SPECTRAL MATRIX METHODS FOR SOCIAL INFLUENCE AND COMMUNITY FORMATION IN COMPLEX NETWORKS

The analysis of social networks has become an important interdisciplinary re-search area involving mathematics, sociology, and computer science. Graph theo-retic models provide useful tools for representing relationships among individuals, yet classical matrix representations often fail to incorporate variations in influence strength within networks.

In this paper, we introduce a matrix-based framework called the Social Influence Spectral Matrix (SISM). The proposed matrix integrates network connectivity, in-fluence weights, and degree-based reinforcement into a unified spectral model. We also introduce a new measure called the Spectral Social Cohesion Index (SSCI) to quantify the strength of community formation in a network.

At the present stage, the study should be viewed as a proposed framework accompanied by preliminary theoretical observations. The results presented here provide motivation for further mathematical investigation and empirical validation in the study of influence dynamics in social networks.