imported>Danhash: /* Tools to deal with networks */ link MATLAB

2024-08-20T18:59:07Z

Tools to deal with networks: link MATLAB

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{{Short description|Hybrid network topology}}{{Distinguish|Tree (data structure)}}

[[File:TreeTopology.png|alt= Tree topology|thumb|Tree network topology]]

A '''tree topology''', or '''star-bus topology''', is a hybrid [[network topology]] in which [[star network]]s are interconnected via [[bus network]]s.<ref>{{cite book |url=https://books.google.com/books?id=gnuwPpBcO-MC&pg=RA1-PT12 |title=Understanding Computer Science (for Advanced Level): The Study Guide |last=Bradley |first=Ray |location=Cheltenham |publisher=[[Nelson Thornes]] |page=244 |isbn=978-0-7487-6147-0 |oclc=47869750 |access-date=2016-03-26}}</ref><ref>{{cite book |title=Networking Bible |last=Sosinsky |first=Barrie A. |page=16 |date=2009 |location=Indianapolis |publisher=Wiley Publishing |isbn=978-0-470-43131-3 |oclc=359673774 |chapter=Network Basics |chapter-url=https://books.google.com/books?id=3DOREqRZejcC&pg=PA16 |access-date=2016-03-26}}</ref> Tree networks are hierarchical, and each [[Node (networking)|node]] can have an arbitrary number of child nodes.

== Regular tree networks==

A regular tree network's topology is characterized by two parameters: the branching, <math>d</math>, and the
number of generations, <math>G</math>. The total number of the nodes, <math>N</math>, and the number of peripheral nodes <math>N_p</math>, are given by <ref>{{cite journal | last1 = Kromer | first1 = J. | last2 = Khaledi-Nasab | first2 = A | last3 = Schimansky-Geier | first3 = L. |last4 = Neiman | first4 = A.B| year = 2017 | title = Emergent stochastic oscillations and signal detection in tree networks of excitable elements | journal = Scientific Reports | volume = 7 | doi=10.1038/s41598-017-04193-8 | arxiv = 1701.01693 }}</ref>

: <math>N= \frac{d^{G+1}-1}{d-1},\quad N_p=d^G</math>

== Random tree networks==
Three parameters are crucial in determining the statistics of random tree networks, first, the branching probability, second the maximum number of allowed progenies at each branching point, and third the maximum number of generations, that a tree can attain. There are a lot of studies that address the large tree networks, however small tree networks are seldom studied.<ref>{{Cite journal |last=Khaledi-Nasab |first=Ali |last2=Kromer |first2=Justus A. |last3=Schimansky-Geier |first3=Lutz |last4=Neiman |first4=Alexander B. |date=2018-11-12 |title=Variability of collective dynamics in random tree networks of strongly coupled stochastic excitable elements |url=https://link.aps.org/doi/10.1103/PhysRevE.98.052303 |journal=Physical Review E |volume=98 |issue=5 |pages=052303 |doi=10.1103/PhysRevE.98.052303|arxiv=1808.02750 }}</ref>

==Tools to deal with networks==

A group at MIT has developed a set of functions for [[MATLAB|Matlab]] that can help in analyzing the networks. These tools could be used to study the tree networks as well.

{{cite web |url=http://strategic.mit.edu/downloads.php?page=matlab_networks |title=MIT Strategic Engineering Research Group (SERG), Part II |last= L. de Weck|first=Oliver |access-date=May 1, 2018}}

==References==
{{Reflist}}

{{Network topologies}}

[[Category:Network topology]]
[[Category:Trees (data structures)]]

Tree network - Revision history

imported>Danhash: /* Tools to deal with networks */ link MATLAB