TY  - RPRT
Y1  - 2015/07//
UR  - http://arxiv.org/abs/1507.04400
M1  - working_paper
A1  - Morrison, Greg
A1  - Dudte, Levi
A1  - Mahadevan, L.
PB  - arXiv
KW  - Physics and Society
KW  -  Social and Information Networks
AV  - public
EP  - 39
ID  - eprints2805
N2  - In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. 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 a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic.
TI  - Generalized Erdos Numbers for network analysis
ER  -