Dataset Information

Generalized Erdos numbers for network analysis.

ABSTRACT: The identification of relationships in complex networks is critical in a variety of scientific contexts. This includes the identification of globally central nodes and analysing the importance of pairwise relationships between nodes. In this paper, we consider the concept of topological proximity (or 'closeness') between nodes in a weighted network using the generalized Erdős numbers (GENs). This measure satisfies a number of desirable properties for networks with nodes that share a finite resource. These include: (i) real-valuedness, (ii) non-locality and (iii) asymmetry. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to new methods to measure centrality. We show that the square of the leading eigenvector of an importance matrix defined using the GENs is strongly correlated with well-known measures such as PageRank, and define a personalized measure of centrality that is also well correlated with other existing measures. The utility of this measure of topological proximity is demonstrated by showing the asymmetries in both the dynamics of random walks and the mean infection time in epidemic spreading are better predicted by the topological definition of closeness provided by the GENs than they are by other measures.

SUBMITTER: Morrison G

PROVIDER: S-EPMC6124095 | biostudies-other | 2018 Aug

REPOSITORIES: biostudies-other

ACCESS DATA

Publications

Generalized Erdős numbers for network analysis.

Morrison Greg G Dudte Levi H LH Mahadevan L L

Royal Society open science 20180829 8

The identification of relationships in complex networks is critical in a variety of scientific contexts. This includes the identification of globally central nodes and analysing the importance of pairwise relationships between nodes. In this paper, we consider the concept of topological proximity (or 'closeness') between nodes in a weighted network using the generalized Erdős numbers (GENs). This measure satisfies a number of desirable properties for networks with nodes that share a finite resou ...[more]

PMID: 30224995

Similar Datasets

Project description:An SEQIJR model of epidemic disease transmission which includes immunization and a varying population size is studied. The model includes immunization of susceptible people (S), quarantine (Q) of exposed people (E), isolation (J) of infectious people (I), a recovered population (R), and variation in population size due to natural births and deaths and deaths of infected people. It is shown analytically that the model has a disease-free equilibrium state which always exists and an endemic equilibrium state which exists if and only if the disease-free state is unstable. A simple formula is obtained for a generalized reproduction number Rg where, for any given initial population, Rg<1 means that the initial population is locally asymptotically stable and Rg>1 means that the initial population is unstable. As special cases, simple formulas are given for the basic reproduction number R0 , a disease-free reproduction number Rdf , and an endemic reproduction number Ren . Formulas are derived for the sensitivity indices for variations in model parameters of the disease-free reproduction number Rdf and for the infected populations in the endemic equilibrium state. A simple formula in terms of the basic reproduction number R0 is derived for the critical immunization level required to prevent the spread of disease in an initially disease-free population. Numerical simulations are carried out using the Matlab program for parameters corresponding to the outbreaks of severe acute respiratory syndrome (SARS) in Beijing, Hong Kong, Canada and Singapore in 2002 and 2003. From the sensitivity analyses for these four regions, the parameters are identified that are the most important for preventing the spread of disease in a disease-free population or for reducing infection in an infected population. The results support the importance of isolating infectious individuals in an epidemic and in maintaining a critical level of immunity in a population to prevent a disease from occurring.

Dataset Information

Generalized Erdos numbers for network analysis.

Publications

Generalized Erdős numbers for network analysis.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets