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Connected graphs with prescribed median and periphery

Steven J. Winters
1996 Discrete Mathematics  
For graphs F and G and a positive integer m, necessary and sufficient conditions are given for F and G to be the median and periphery, respectively, of some connected graph such that the distance between  ...  the median and periphery is m.  ...  Thus, F is a complete graph. [] Connected graphs with intersecting median and periphery Let F1, Fz, and K be graphs with K isomorphic to an induced subgraph of both F1 and F2.  ... 
doi:10.1016/0012-365x(95)00080-g fatcat:bk6xkx2fg5bb7oyuxxnyjpni4y

Page 4745 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
Slater (1-ALH) 92i:05090 05C12 05C20 Chartrand, Gary (1-WMI); Tian, Song Lin (1-CMOS) Oriented graphs with prescribed m-center and m-median. Czechoslovak Math. J. 41(116) (1991), no. 4, 716-723.  ...  with lengths d, e and /, respectively, and K, a complete graph on k vertices.  ... 

Page 4068 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
972:05086 97g:05086 05C20 05C12 Bertz, Lyle (1-CMOS; Warrensburg, MO); Tian, Songlin (1-CMOS; Warrensburg, MO) Asymmetric digraphs with prescribed m-median and m-periphery. (English summary) J.  ...  The paper deals with computations of these median orders. First, improvements of a branch and bound method to speed up the enumeration of median orders is presented.  ... 

Prescribing Associated with High-Risk Opioid Exposures Among Non-cancer Chronic Users of Opioid Analgesics: a Social Network Analysis

Keiki Hinami, Michael J. Ray, Kruti Doshi, Maria Torres, Steven Aks, John J. Shannon, William E. Trick
2019 Journal of general internal medicine  
despite a steady decline in the number of individual prescriptions directing ≥ 90 morphine milligram equivalents (MME)/day may be explained by patient exposures to redundant prescriptions from multiple prescribers  ...  The heat map display was hierarchically sorted along the x-and y-axes by k-shell/core (quantitatively strongest connections displayed in the top left section of the graph) and number of opioid prescription  ...  Because the prescriber-beneficiary social network using our data is comprised of a highly connected small group of central nodes surrounded by nodes with decreasing centrality toward the periphery, we  ... 
doi:10.1007/s11606-019-05114-3 pmid:31420823 pmcid:PMC6848735 fatcat:ds2hixp77zch5mqi4oedtjxgua

Page 6180 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
Winters, Strong asymmetric digraphs with prescribed median and periphery (61- 73); Marco Valtorta and M. Ishaq Zahid, Tie-breaking rules for 4x n Warnsdorffs tours (75-86); Robert E.  ...  Palmer, The enu- meration of trees with certain local restrictions (183-202); Yingiu Luo and Jie Wu, Gray-code-based cube-connected cubes (203- 211); Renée A. McCauley and W. R.  ... 

Towards a new approach to reveal dynamical organization of the brain using topological data analysis

Manish Saggar, Olaf Sporns, Javier Gonzalez-Castillo, Peter A. Bandettini, Gunnar Carlsson, Gary Glover, Allan L. Reiss
2018 Nature Communications  
Using existing multitask fMRI datasets, with the known ground truth about the timing of transitions from one task-block to next, our approach tracks both within-and between-task transitions at a much faster  ...  In summary, our approach distills complex brain dynamics into interactive and behaviorally relevant representations.  ...  Two groups were formed using a median split based on the overall task performance (low (n = 9) and high performers (n = 9) with a median split at 86.9% accuracy).  ... 
doi:10.1038/s41467-018-03664-4 pmid:29643350 pmcid:PMC5895632 fatcat:cxbund33zjbf3ilvlenezp5rye

Stability of spontaneous, correlated activity in mouse auditory cortex

Richard F. Betzel, Katherine C. Wood, Christopher Angeloni, Maria Neimark Geffen, Danielle S. Bassett, Lyle Muller
2019 PLoS Computational Biology  
The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system's topological organization and to better understand its function.  ...  Finally, we show that a small fraction of cells maintain strongly-correlated activity over multiple days, forming a stable temporal core surrounded by a fluctuating and variable periphery.  ...  The notion of a network in its simplest form is akin to the notion of a graph in the field of mathematics known as graph theory [19] .  ... 
doi:10.1371/journal.pcbi.1007360 pmid:31815941 pmcid:PMC6968873 fatcat:pnkibdlbsnak5phg3chvf3mfui

Monophonic Distance in Graphs [chapter]

P. Titus, A.P. Santhakumaran
2018 Graph Theory - Advanced Algorithms and Applications  
For any two vertices u and v in a connected graph G, a u − v path is a monophonic path if it contains no chords, and the monophonic distance d m (u, v) The subgraph induced by the vertices of G having  ...  Also it is proved that the monophonic center of every connected graph G lies in some block of G.  ...  [35] that a connected graph G of order p ≥ 3 and radius 1 is the detour periphery of some connected graph if and only if G is Hamiltonian.  ... 
doi:10.5772/intechopen.68668 fatcat:ce4s6h4k4nbqdn7r473g6s7nhe

MONOPHONIC DISTANCE IN GRAPHS

A. P. SANTHAKUMARAN, P. TITUS
2011 Discrete Mathematics, Algorithms and Applications (DMAA)  
For any two vertices u and v in a connected graph G, a u − v path is a monophonic path if it contains no chords, and the monophonic distance d m (u, v) The subgraph induced by the vertices of G having  ...  Also it is proved that the monophonic center of every connected graph G lies in some block of G.  ...  [35] that a connected graph G of order p ≥ 3 and radius 1 is the detour periphery of some connected graph if and only if G is Hamiltonian.  ... 
doi:10.1142/s1793830911001176 fatcat:o7yyuukiynad3mtx4xvnjcs4ee

Stability of spontaneous, correlated activity in mouse auditory cortex [article]

Richard Betzel, Katherine C Wood, Christopher Angeloni, Maria Neimark Geffen, Danielle S Bassett
2018 bioRxiv   pre-print
The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system's topological organization and to better understand its function.  ...  Finally, we show that a small fraction of cells maintain strongly-correlated activity over multiple days, forming a stable temporal core surrounded by a fluctuating and variable periphery.  ...  ACKNOWLEDGEMENTS RFB and DSB would like to acknowledge support from the John D. and Catherine T. MacArthur Foundation, the Alfred P. Sloan Foundation, the Army Re-  ... 
doi:10.1101/491936 fatcat:5pgx5f5sgnar5iedgxwxluaonq

Stability of spontaneous, correlated activity in mouse auditory cortex [article]

Richard F. Betzel, Katherine C. Wood, Christopher Angeloni, Maria Neimark Geffen, Danielle S. Bassett
2018 arXiv   pre-print
The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system's topological organization and to better understand its function.  ...  Neural systems can be modeled as networks of functionally connected neural elements.  ...  ACKNOWLEDGEMENTS RFB and DSB would like to acknowledge support from the John D. and Catherine T. MacArthur Foundation, the Alfred P.  ... 
arXiv:1812.03796v1 fatcat:u24f3auuuzanlfadstnsta6zny

Comparative study of human cancellous bone remodeling to titanium and hydroxyapatite-coated implants

Aaron A. Hofmann, Kent N. Bachus, Roy D. Bloebaum
1993 Journal of Arthroplasty  
Ti HA MAR Periphery (um/day) > oy 21 CnNAuURWN = ——_ +O + + F Fm — Co _ oO w Population median Estimate of median difference +t 95% confidence interval P .999 .180 * Patients noncompliant with oxytetracycline  ...  prior to the second prescribed TKA surgery and subse- quent implant removal.  ... 
doi:10.1016/s0883-5403(06)80056-2 pmid:8386746 fatcat:3orv6nn2grga5imp4ghgzndxjy

Core-periphery or decentralized? Topological shifts of specialized information on Twitter

Marco Bastos, Carlo Piccardi, Michael Levy, Neil McRoberts, Mark Lubell
2018 Social Networks  
For the purposes of this study, we refer to subgraphs as a defined set of nodes and arcs of the original Twitter graph selected on the basis of specific characteristics of the message.  ...  Highlights • Twitter agriculture social web is modelled with the core-periphery profile approach • Network centralization increases when Twitter users share specialized information • Network shifts from  ...  Maximum and minimum core-periphery scores C across communities were .73 and .87 (mean x̄=.78, median x=.77, and standard deviation σ=.04), compared with .60 and .72 for the randomized subgraphs (x̄=.67  ... 
doi:10.1016/j.socnet.2017.09.006 fatcat:po6gshmfi5brdp52nkfniv7v7q

Fragmented Networks and Entrepreneurship in Late Imperial Russia

Henning Hillmann, Brandy L. Aven
2010 Social Science Research Network  
In contrast, founders are less constrained when they join with partners who are otherwise not connected with each other.  ...  For the graphing layout, see the note to figure 2. Fig. 4 . 4 -Comparison of network core and periphery: Proportion of cofounding ties within categories over entire period, 1869-1913.  ... 
doi:10.2139/ssrn.1422784 fatcat:vxal2etkjjdorgetnklmow7g2a

Fragmented Networks and Entrepreneurship in Late Imperial Russia

Henning Hillmann, Brandy L. Aven
2011 American Journal of Sociology  
In contrast, founders are less constrained when they join with partners who are otherwise not connected with each other.  ...  For the graphing layout, see the note to figure 2. Fig. 4 . 4 -Comparison of network core and periphery: Proportion of cofounding ties within categories over entire period, 1869-1913.  ... 
doi:10.1086/661772 fatcat:z2vswjfjpjeqje6ub6lktgjmxa
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