We study treatment effect modifiers for causal analysis in a social network, where neighbors' characteristics or network structure may affect the outcome of a unit, and the goal is to identify sub-populations with varying treatment effects using such network properties. We propose a novel framework for this purpose that facilitates data-driven decision making by testing hypotheses about complex effect modifiers in terms of network features or network patterns (e.g., characteristics of neighbors of a unit or belonging to a triangle), and by identifying sub-populations for which a treatment is likely to be effective or harmful. We describe a hypothesis testing approach that accounts for a unit's covariates, their neighbors' covariates, and patterns in the social network, and devise an algorithm incorporating ideas from causal inference, hypothesis testing, and graph theory to verify a hypothesized effect modifier. In addition, we develop a novel algorithm for the discovery of network patterns that are potential effect modifiers. We perform extensive experimental evaluations with a real development economics dataset about the treatment effect of belonging to a financial support network called self-help groups on risk tolerance, and also with a synthetic dataset with known ground truths simulating a vaccine efficacy trial, to evaluate our framework and algorithms.