There is an error in Fig. 2, " Matching components in a weighted bipartite graph. " Please see the corrected Fig. 2 here. Fig 2. Matching components in a weighted bipartite graph. open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cr...

We define a new weighted zeta function for finite graph and obtain its determinant expression. This result gives the characteristic polynomial of transition matrix Szegedy walk on graph.

Extracting spatial-temporal knowledge from data is useful in many applications. It important that the obtained human-interpretable and amenable to formal analysis. In this letter, we propose a method trains neural networks learn properties form of weighted graph-based signal temporal logic (w-G...

A parametric weighted graph is a graph whose edges are labeled with continuous real functions of a single common variable. For any instantiation of the variable, one obtains a standard edgeweighted graph. Parametric weighted graph problems are generalizations of weighted graph problems, and arise in various natural scenarios. Parametric weighted graph algorithms consist of two phases. A preproc...