As user interact with social media spaces, like twitter they form connections that emerge into complex social network structures. This article proposes a conceptual and practical model for the classification of topical Twitter networks based on their network-level structures. These connections are indicators of content sharing, and network structures reflect patterns of information flow. As current literature focuses on the classification of users to key positions, this study utilizes the overall network structures In order to classify Twitter conversation based on their patterns of information flow. Four network level metrics which have been established as indicators of information flow characteristics density, modularity, centralization and the fraction of isolated users-are utilized in a three step classification model. This process led us to suggest six structures of information flow, divided, inified , fragmented ,clustered in and out hub and spoke networks. We demonstrate the value of these network structure by segmenting 60 Twitter topical social media network dataset’s into these six distinct patterns of collective connections. We discuss conceptual and practical implications of each structure.