Convolutional Graph-Tensor Net for Graph Data Completion

Graph data completion is a fundamentally important issue as data generally has a graph structure, e.g., social networks, recommendation systems, and the Internet of Things. We consider a graph where each node has a data matrix, represented as a \textit{graph-tensor} by stacking the data matrices in the third dimension. In this paper, we propose a \textit{Convolutional Graph-Tensor Net} (\textit{Conv GT-Net}) for the graph data completion problem, which uses deep neural networks to learn the general transform of graph-tensors. The experimental results on the ego-Facebook data sets show that the proposed \textit{Conv GT-Net} achieves significant improvements on both completion accuracy (50\% higher) and completion speed (3.6x $\sim$ 8.1x faster) over the existing algorithms

Influence of Reciprocal links in Social Networks

In this Letter, we empirically study the influence of reciprocal links, in order to understand its role in affecting the structure and function of directed social networks. Experimental results on two representative datesets, Sina Weibo and Douban, demonstrate that the reciprocal links indeed play a more important role than non-reciprocal ones in both spreading information and maintaining the network robustness. In particular, the information spreading process can be significantly enhanced by considering the reciprocal effect. In addition, reciprocal links are largely responsible for the connectivity and efficiency of directed networks. This work may shed some light on the in-depth understanding and application of the reciprocal effect in directed online social networks

The spectral radius of minor free graphs

In this paper, we present a sharp upper bound for the spectral radius of an $n$-vertex graph without $F$-minor for sufficient large $n$, where $F$ is obtained from the complete graph $K_r$ by deleting disjointed paths. Furthermore, the graphs which achieved the sharp bound are characterized. This result may be regarded to be an extended revision of the number of edges in an $n$-vertex graph without $F$-minor.Comment: 18 pages, 1 figur