Beyond the shortest path: the path length index as a distribution

10/06/2022
by   Leonardo B L Santos, et al.
0

The traditional complex network approach considers only the shortest paths from one node to another, not taking into account several other possible paths. This limitation is significant, for example, in urban mobility studies. In this short report, as the first steps, we present an exhaustive approach to address that problem and show we can go beyond the shortest path, but we do not need to go so far: we present an interactive procedure and an early stop possibility. After presenting some fundamental concepts in graph theory, we presented an analytical solution for the problem of counting the number of possible paths between two nodes in complete graphs, and a depth-limited approach to get all possible paths between each pair of nodes in a general graph (an NP-hard problem). We do not collapse the distribution of path lengths between a pair of nodes into a scalar number, we look at the distribution itself - taking all paths up to a pre-defined path length (considering a truncated distribution), and show the impact of that approach on the most straightforward distance-based graph index: the walk/path length.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/18/2020

Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters

The Minimum Eccentricity Shortest Path Problem consists in finding a sho...
research
12/02/2022

PSPC: Efficient Parallel Shortest Path Counting on Large-Scale Graphs

In modern graph analytics, the shortest path is a fundamental concept. N...
research
09/18/2020

Length-Bounded Paths Interdiction in Continuous Domain for Network Performance Assessment

Studying on networked systems, in which a communication between nodes is...
research
04/28/2021

SMLSOM: The shrinking maximum likelihood self-organizing map

Determining the number of clusters in a dataset is a fundamental issue i...
research
06/05/2018

Estimating Shortest Path Length Distributions via Random Walk Sampling

In a network, the shortest paths between nodes are of great importance a...
research
10/22/2019

Simplification of networks via conservation of path diversity and minimisation of the search information

Alternative paths in a network play an important role in its functionali...
research
09/01/2015

Iterative hypothesis testing for multi-object tracking in presence of features with variable reliability

This paper assumes prior detections of multiple targets at each time ins...

Please sign up or login with your details

Forgot password? Click here to reset