Most network data are collected from only partially observable networks with both missing nodes and edges, for example due to limited resources and privacy settings specified by users on social media. Thus, it stands to the reason that inferring the missing parts of the networks by performing completion should precede downstream mining or learning tasks on the networks. However, despite this need, the recovery of missing nodes and edges in such incomplete networks is an insufficiently explored problem. In this paper, we present DeepNC, a novel method for inferring the missing parts of a network that is based on a deep generative graph model. Specifically, our model first learns a likelihood over edges via a recurrent neural network (RNN)-based generative graph, and then identifies the graph that maximizes the learned likelihood conditioned on the observable graph topology. Moreover, we propose a computationally efficient DeepNC algorithm that consecutively finds a single node to maximize the probability in each node generation step, whose runtime complexity is almost linear in the number of nodes in the network. We empirically show the superiority of DeepNC over state-of-the-art network completion approaches on a variety of synthetic and real-world networks.
A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L sub 1 norm and then transforming the resulting quadratic optimization problem to a linear one. The linear program is solved using a simplex-based algorithm. Then, approximate 0-1 integer solutions are obtained by applying the Hungarian method on the real solutions of the linear program. The complexity of the proposed algorithm is polynomial time, and it is O(n sup 6 L) for matching graphs of size n. The developed algorithm is compared to two other algorithms. One is based on an eigendecomposition approach and the other on a symmetric polynomial transform. Experimental results showed that the LP approach is superior in matching graphs than both other methods. >