let $g$ be a graph and let $m_{ij}(g)$, $i,jge 1$, be the number of edges $uv$ of $g$ such that ${d_v(g), d_u(g)} = {i,j}$. the {em $m$-polynomial} of $g$ is introduced with $displaystyle{m(g;x,y) = sum_{ile j} m_{ij}(g)x^iy^j}$. it is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular ca...

Graph-oriented methods have been widely adopted in multi-view clustering because of their efficiency learning heterogeneous relationships and complex structures hidden data. However, existing are typically investigated based on a Euclidean structure instead more suitable manifold topological structure. Hence, it is expected that will be to carry out intrinsic similarity learning. In this paper,...

Graph neural networks have emerged as a powerful representation learning model for undertaking various graph prediction tasks. Various pooling methods been developed to coarsen an input into succinct graph-level through aggregating node embeddings obtained via convolution. However, because most are heavily node-centric, they fail fully leverage the crucial information contained in structure. Th...

This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computa-tionally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools...

Facial Beauty Prediction (FBP) is an important visual recognition problem to evaluate the attractiveness of faces according human perception. Most existing FBP methods are based on supervised solutions using geometric or deep features. Semi-supervised learning for almost unexplored research area. In this work, we propose a graph-based semi-supervised method in which multiple graphs constructed ...

The dynamic behavior of rule-based systems (like term rewriting systems 24], process algebras 27], and so on) can be traditionally determined in two orthogonal ways. Either operationally, in the sense that a way of embedding a rule into a state is devised, stating explicitly how the result is built: This is the role played by (the application of) a substitution in term rewriting. Or inductively...

This paper presents a view{based approach to map learning and navigation in mazes. By means of graph theory we have shown that the view{graph is a suucient representation for map behaviour such as path planning. A neural network for unsupervised learning of the view{graph from sequences of views is constructed. We use a modiied Kohonen (1988) learning rule that transforms temporal sequence (rat...

This paper presents a view based approach to map learning and nav igation in mazes By means of graph theory we have shown that the view graph is a su cient representation for map behaviour such as path planning A neural network for unsupervised learning of the view graph from sequences of views is constructed We use a modi ed Kohonen learning rule that transforms temporal sequence rather than f...