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Dynamic networks have intrinsic structural, computational, and multidisciplinary advantages. Link prediction estimates the next relationship in dynamic networks. However, in the current link prediction approaches, only bipartite or non-bipartite but homogeneous networks are considered. The use of adjacency matrix to represent dynamically evolving networks limits the ability to analytically learn from heterogeneous, sparse, or forming networks. In the case of a heterogeneous network, modeling all network states using a binary-valued matrix can be difficult. On the other hand, sparse or currently forming networks have many missing edges, which are represented as zeros, thus introducing class imbalance or noise. We propose a time-parameterized matrix (TP-matrix) and empirically demonstrate its effectiveness in non-bipartite, heterogeneous networks. In addition, we propose a predictive influence index as a measure of a node's boosting or diminishing predictive influence using backward and forward-looking maximization over the temporal space of the n-degree neighborhood. We further propose a new method of canonically representing heterogeneous time-evolving activities as a temporally parameterized network model (TPNM). The new method robustly enables activities to be represented as a form of a network, thus potentially inspiring new link prediction applications, including intelligent business process management systems and context-aware workflow engines. We evaluated our model on four datasets of different network systems. We present results that show the proposed model is more effective in capturing and retaining temporal relationships in dynamically evolving networks. We also show that our model performed better than state-of-the-art link prediction benchmark results for networks that are sensitive to temporal evolution.