Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions
نویسندگان
چکیده
منابع مشابه
Epidemic Outbreaks in Networks with Equitable or Almost-Equitable Partitions
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals infect those belonging to the same community with higher probability than individuals in other communities. In community models the nodal infection probabili...
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We consider two kinds of partition of a graph, namely orbit partitions and equitable partitions. Although an orbit partition is always an equitable partition, the converse is not true in general. We look at some classes of graphs for which the converse is true.
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Relations between Laplacian eigenvectors and eigenvalues and the existence of almost equitable partitions (which are generalizations of equitable partitions) are presented. Furthermore, on the basis of some properties of the adjacency eigenvectors of a graph, a necessary and sufficient condition for the graph to be primitive strongly regular is introduced. c © 2006 Elsevier Ltd. All rights rese...
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In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one may generalize that concept as a block partition of a complex square matrix s.t. each block has constant row sum. It is well known that replacing each block ...
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Significant progress has recently been made towards formalizing symmetry-aware variational inference approaches into a coherent framework. With the exception of TRW for marginal inference, however, this framework resulted in approximate MAP algorithms only, based on equitable and orbit partitions of the graphical model. Here, we deepen our understanding of it for marginal inference. We show tha...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Mathematics
سال: 2015
ISSN: 0036-1399,1095-712X
DOI: 10.1137/140995829