Maximally Fault Tolerant Directed Network Graph with Sublogarithmic Diameter for Arbitrary Number of Nodes

1993 ◽  
Author(s):  
Pradip K Srimani
Keyword(s):  
Arbitrary Number ◽  
Fault Tolerant ◽  
Directed Network ◽  
Network Graph

SUPER ROTATOR: INCREMENTALLY EXTENSIBLE DIRECTED NETWORK GRAPH OF SUBLOGARITHMIC DIAMETER

1996 ◽  
Vol 06 (04) ◽  
pp. 479-490
Author(s):  
PRADIP K. SRIMANI
Keyword(s):  
Arbitrary Number ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Directed Network ◽  
Constant Independent ◽  
Network Graph ◽  
New Family ◽  
The Difference

We propose a new family of directed interconnection network graphs for an arbitrary number of nodes. The proposed network graph is almost regular (the difference between the in-degrees and out degrees of nodes is 2, a constant independent of the size of the network), has a diameter sub logarithmic in the number of nodes, is optimally fault tolerant and can be defined for an arbitrary number of nodes.

Abstract P214: Social Network Analysis of a Community Aphasia Group Pre- And Post-Covid: Implications for Future Planning

Stroke ◽  
2021 ◽  
Vol 52 (Suppl_1) ◽  
Author(s):  
Tom Sather ◽  
Anna Livera
Keyword(s):  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Time Frame ◽  
Directed Network ◽  
Negative Consequences ◽  
Network Graph ◽  
Future Planning ◽  
Network Characteristics ◽  
The Impact

Introduction: Among the many negative consequences of aphasia is an altered social network. Social network analysis supports an objective, quantitative evaluation of social networks among individuals with aphasia along with potential impacts of social programming and interventions on an individual’s social network. Social network analysis may also support better understanding of the impact of Covid on individuals with aphasia. Aims: This pilot evaluation utilized social network analysis via R to evaluate the social network characteristics of a community-based aphasia network across a 12-month pre-Covid period. Social network aphasia group data for a standard duration of time pre- and post-Covid were also compared to identify potential social implications of Covid in a population already at higher risk for reduced social interactions. This presentation will also provide fundamental concepts relevant to social network analysis for those interested in pursuing such analysis in further depth. Methods: Twelve months of pre-Covid aphasia group program attendance data were examined using the visNetwork R package. An additional six months of Covid-era time frame data were also analyzed.The primary relationship function of “ a attended b” (where a = individual participant and b = event/setting) was used in the analysis. Multiple social network characteristics were analyzed and displayed including node, edgeness, directionality, weight, and centrality indices across individuals with aphasia, care partners and community members and settings. Results and Conclusions: Network analysis reveals a directed network graph with primarily unidirectional relationships. There is an emergence of several aphasia group participant behavior types, both pre- and post-Covid, relevant for future planning including: communities of individuals who have similar behaviors in terms of type of event attendance; key individuals who are "heavy users" of various services in terms of frequency and breadth of event attendance; and peripheral users who use only one service. Post-Covid social network implications are discussed including supports to mitigate negative impacts of Covid on social network composition.

scholarly journals Premagic and Ideal Flow Matrices

2019 ◽  
Vol 3 (1) ◽  
pp. 35-45
Author(s):  
Kardi Teknomo
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Directed Graph ◽  
Directed Network ◽  
Network Graph ◽  
Ideal Flow ◽  
Strongly Connected

Several interesting properties of a special type of matrix that has a row sum equal to the column sum are shown with the proofs. Premagic matrix can be applied to strongly connected directed network graph due to its nodes conservation flow. Relationships between Markov Chain, ideal flow and random walk on directed graph are also discussed.

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