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Coarse-graining and self-dissimilarity of complex networks Shalev Itzkovitz, Reuven Levitt, Nadav Kashtan, Ron Milo, Michael Itzkovitz, and Uri Alon
 

Summary: Coarse-graining and self-dissimilarity of complex networks
Shalev Itzkovitz, Reuven Levitt, Nadav Kashtan, Ron Milo, Michael Itzkovitz, and Uri Alon
Departments of Molecular Cell Biology and Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel 76100
Received 13 May 2004; revised manuscript received 21 July 2004; published 21 January 2005
Can complex engineered and biological networks be coarse-grained into smaller and more understandable
versions in which each node represents an entire pattern in the original network? To address this, we define
coarse-graining units as connectivity patterns which can serve as the nodes of a coarse-grained network and
present algorithms to detect them. We use this approach to systematically reverse-engineer electronic circuits,
forming understandable high-level maps from incomprehensible transistor wiring: first, a coarse-grained ver-
sion in which each node is a gate made of several transistors is established. Then the coarse-grained network
is itself coarse-grained, resulting in a high-level blueprint in which each node is a circuit module made of many
gates. We apply our approach also to a mammalian protein signal-transduction network, to find a simplified
coarse-grained network with three main signaling channels that resemble multi-layered perceptrons made of
cross-interacting MAP-kinase cascades. We find that both biological and electronic networks are "self-
dissimilar," with different network motifs at each level. The present approach may be used to simplify a variety
of directed and nondirected, natural and designed networks.
DOI: 10.1103/PhysRevE.71.016127 PACS number s : 89.75.Fb
I. INTRODUCTION
In both engineering and biology it is of interest to under-
stand the design of complex networks 13 , a task known as

  

Source: Alon, Uri - Departments of Molecular Cell Biology & Physics of Complex Systems, Weizmann Institute of Science

 

Collections: Biology and Medicine