Discriminative Distance-Based Network Indices with Application to Link Prediction

In large networks, using the length of shortest paths as the distance measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs and directed graphs is controversial. The second shortcoming is that a huge number of vertices may have exactly the same score. The third shortcoming is that in many applications, the distance between two vertices not only depends on the length of shortest paths, but also on the number of shortest paths. In this paper, first we develop a new distance measure between vertices of a graph that yields discriminative distance-based centrality indices. This measure is proportional to the length of shortest paths and inversely proportional to the number of shortest paths. We present algorithms for exact computation of the proposed discriminative indices. Second, we develop randomized algorithms that precisely estimate average discriminative path length and average discriminative eccentricity and show that they give $(\epsilon,\delta)$-approximations of these indices. Third, we perform extensive experiments over several real-world networks from different domains. In our experiments, we first show that compared to the traditional indices, discriminative indices have usually much more discriminability. Then, we show that our randomized algorithms can very precisely estimate average discriminative path length and average discriminative eccentricity, using only few samples. Then, we show that real-world networks have usually a tiny average discriminative path length, bounded by a constant (e.g., 2). Fourth, in order to better motivate the usefulness of our proposed distance measure, we present a novel link prediction method, that uses discriminative distance to decide which vertices are more likely to form a link in future, and show its superior performance compared to the well-known existing measures

Comparative research on all to all pairs path finding algorithms in a real-world scenario

This paper presents a comparative study of the implementation of all-to-all pairs shortest path algorithms, specifically Floyd-Warshall, Johnson’s, and Dijkstra’s. It contributes to a better understanding of their strengths and weaknesses in different types of applications (real-world scenarios). The research demonstrates the use of these algorithms in finding the shortest path between multiple locations using a Google Maps plotter and the Google Maps API. Older research papers have shown a comparison that shows that the Floyd-Warshall algorithm is faster than the other two algorithms in certain scenarios; however, none have brought up the real-world application of such an algorithm. The null hypothesis of this study is that the Floyd-Warshall algorithm is not suitable for use in a real-life application for finding the shortest path compared to Johnson’s algorithm. The results of this study have potential applications in transportation and logistics and will provide useful insights for future work in this field

The STEM Methodology and Graph Theory: Some Practical Examples

[EN] In this paper, we highlight that Graph Theory is certainly well suited to an applications approach. One of the basic problems that this theory solves is finding the shortest path between two points. For this purpose, we propose two real-world problems aimed at STEM undergraduate students to be solved by using shortest path algorithms from Graph Theory after previous modeling.Jordan-Lluch, C.; Murillo Arcila, M.; Torregrosa Sánchez, JR. (2021). The STEM Methodology and Graph Theory: Some Practical Examples. Mathematics. 9(23):1-10. https://doi.org/10.3390/math9233110S11092

Efficient Computation of Distance Labeling for Decremental Updates in Large Dynamic Graphs

Since today's real-world graphs, such as social network graphs, are evolving all the time, it is of great importance to perform graph computations and analysis in these dynamic graphs. Due to the fact that many applications such as social network link analysis with the existence of inactive users need to handle failed links or nodes, decremental computation and maintenance for graphs is considered a challenging problem. Shortest path computation is one of the most fundamental operations for managing and analyzing large graphs. A number of indexing methods have been proposed to answer distance queries in static graphs. Unfortunately, there is little work on answering such queries for dynamic graphs. In this paper, we focus on the problem of computing the shortest path distance in dynamic graphs, particularly on decremental updates (i.e., edge deletions). We propose maintenance algorithms based on distance labeling, which can handle decremental updates efficiently. By exploiting properties of distance labeling in original graphs, we are able to efficiently maintain distance labeling for new graphs. We experimentally evaluate our algorithms using eleven real-world large graphs and confirm the effectiveness and efficiency of our approach. More specifically, our method can speed up index re-computation by up to an order of magnitude compared with the state-of-the-art method, Pruned Landmark Labeling (PLL)

Finding Distance-Preserving Subgraphs in Large Road Networks

Abstract-Given two sets of points, S and T , in a road network, G, a distance-preserving subgraph (DPS) query returns a subgraph of G that preserves the shortest path from any point in S to any point in T . DPS queries are important in many real world applications, such as route recommendation systems, logistics planning, and all kinds of shortest-path-related applications that run on resource-limited mobile devices. In this paper, we study efficient algorithms for processing DPS queries in large road networks. Four algorithms are proposed with different tradeoffs in terms of DPS quality and query processing time, and the best one is a graph-partitioning based index, called RoadPart, that finds a high quality DPS with short response time. Extensive experiments on large road networks demonstrate the merits of our algorithms, and verify the efficiency of RoadPart for finding a high-quality DPS