Path weights in concentration graphs

Sankey Arcs - Visualizing edge weights in path graphs

Arc diagrams allow exploring relations and their strength between sequential nodes. Previous solutions suffer from displaying all arcs at the center of a node, which can lead to visual obstruction. We present a new technique, which extends the arc diagram technique by laying out the weighted edges of a node adjacent to each other. The aim of our Sankey Arc technique is to improve clarity, to en...

Extremal graphs for weights

From Path Graphs to Directed Path Graphs

We present a linear time algorithm to greedily orient the edges of a path graph model to obtain a directed path graph model (when possible). Moreover we extend this algorithm to find an odd sun when the method fails. This algorithm has several interesting consequences concerning the relationship between path graphs and directed path graphs. One is that for a directed path graph, path graph mode...

The Next-to-Shortest Path in Undirected Graphs with Nonnegative Weights

Given an edge-weighted undirected graph and two vertices s and t, the next-to-shortest path problem is to find an st-path whose length is minimum among all st-paths of lengths strictly larger than the shortest path length. The problem is shown to be polynomially solvable if all edge weights are positive, while the complexity status for the nonnegative weight case was open. In this paper we show...

A Polynomial-Time Algorithm for the Next-to-Shortest Path in Undirected Graphs with Nonnegative Weights

Given an edge-weighted undirected graph and two vertices s and t, the next-to-shortest path problem is to find an st-path whose length is minimum among all st-paths of lengths strictly larger than the shortest path length. The problem is shown to be polynomially solvable if all edge weights are positive, while the complexity status for the nonnegative weight case was open. In this paper we show...