Odd-Graceful Total Colorings for Constructing Graphic Lattice

The security of passwords generated by the graphic lattices is based on the difficulty of the graph isomorphism, graceful tree conjecture, and total coloring conjecture. A graphic lattice is generated by a graphic base and graphical operations, where a graphic base is a group of disjointed, connected graphs holding linearly independent properties. We study the existence of graphic bases with odd-graceful total colorings and show graphic lattices by vertex-overlapping and edge-joining operations; we prove that these graphic lattices are closed to the odd-graceful total coloring.

An efficient procedure for mining egocentric temporal motifs

Temporal graphs are structures which model relational data between entities that change over time. Due to the complex structure of data, mining statistically significant temporal subgraphs, also known as temporal motifs, is a challenging task. In this work, we present an efficient technique for extracting temporal motifs in temporal networks. Our method is based on the novel notion of egocentric temporal neighborhoods, namely multi-layer structures centered on an ego node. Each temporal layer of the structure consists of the first-order neighborhood of the ego node, and corresponding nodes in sequential layers are connected by an edge. The strength of this approach lies in the possibility of encoding these structures into a unique bit vector, thus bypassing the problem of graph isomorphism in searching for temporal motifs. This allows our algorithm to mine substantially larger motifs with respect to alternative approaches. Furthermore, by bringing the focus on the temporal dynamics of the interactions of a specific node, our model allows to mine temporal motifs which are visibly interpretable. Experiments on a number of complex networks of social interactions confirm the advantage of the proposed approach over alternative non-egocentric solutions. The egocentric procedure is indeed more efficient in revealing similarities and discrepancies among different social environments, independently of the different technologies used to collect data, which instead affect standard non-egocentric measures.

Corrigendum to: V. V. Vasilchikov, “Parallel Algorithm for Solving the Graph Isomorphism Problem”, Modeling and analysis of information systems, vol. 27, no. 1, pp. 86–94, 2020. DOI: https://doi.org/10.18255/1818-1015-2020-1-86-94

In the article by V. V. Vasilchikov “Parallel Algorithm for Solving the Graph Isomorphism Problem” ( Modeling and analysis of information systems, vol. 27, no. 1, pp. 86–94, 2020; DOI: https://doi.org/10.18255/1818-1015-2020-1-86-94) there was a misprint in the layout. In the Table 1, in the last column of the row “Degree of graph” the value should be 3000 (instead of 300). The corrected “Table 1” is shown below. The editors apologise for the inconvenience.

Improved Lipophilicity and Aqueous Solubility Prediction with Composite Graph Neural Networks

The accurate prediction of molecular properties, such as lipophilicity and aqueous solubility, are of great importance and pose challenges in several stages of the drug discovery pipeline. Machine learning methods, such as graph-based neural networks (GNNs), have shown exceptionally good performance in predicting these properties. In this work, we introduce a novel GNN architecture, called directed edge graph isomorphism network (D-GIN). It is composed of two distinct sub-architectures (D-MPNN, GIN) and achieves an improvement in accuracy over its sub-architectures employing various learning, and featurization strategies. We argue that combining models with different key aspects help make graph neural networks deeper and simultaneously increase their predictive power. Furthermore, we address current limitations in assessment of deep-learning models, namely, comparison of single training run performance metrics, and offer a more robust solution.

A Polynomial Time Algorithm for Graph Isomorphism and Automorphism

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.