scholarly journals Long Paths and Cycles Passing Through Specified Vertices Under the Average Degree Condition

2015 ◽  
Vol 32 (1) ◽  
pp. 279-295
Author(s):  
Binlong Li ◽  
Bo Ning ◽  
Shenggui Zhang
Keyword(s):  
Average Degree ◽  
Degree Condition ◽  
Long Paths

scholarly journals Note on Long Paths in Eulerian Digraphs

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Charlotte Knierim ◽  
Maxime Larcher ◽  
Anders Martinsson
Keyword(s):  
Recent Result ◽  
Short Note ◽  
Average Degree ◽  
Logarithmic Factor ◽  
Long Paths

Long paths and cycles in Eulerian digraphs have received a lot of attention recently. In this short note, we show how to use methods from [Knierim, Larcher, Martinsson, Noever, JCTB 148:125--148] to find paths of length $d/(\log d+1)$ in Eulerian digraphs with average degree $d$, improving  the recent result of $\Omega(d^{1/2+1/40})$. Our result is optimal up to at most a logarithmic factor.  

scholarly journals Long Paths and Cycles in Random Subgraphs of $\mathcal{H}$-Free Graphs

10.37236/3198 ◽  
2014 ◽  
Vol 21 (1) ◽  
Author(s):  
Michael Krivelevich ◽  
Wojciech Samotij
Keyword(s):  
Random Graph ◽  
Classical Result ◽  
Minimum Degree ◽  
Average Degree ◽  
Free Graph ◽  
Connected Graphs ◽  
Random Subgraph ◽  
Minimum Number ◽  
Random Subgraphs ◽  
Long Paths

Let $\mathcal{H}$ be a given finite (possibly empty) family of connected graphs, each containing a cycle, and let $G$ be an arbitrary finite $\mathcal{H}$-free graph with minimum degree at least $k$. For $p \in [0,1]$, we form a $p$-random subgraph $G_p$ of $G$ by independently keeping each edge of $G$ with probability $p$. Extending a classical result of Ajtai, Komlós, and Szemerédi, we prove that for every positive $\varepsilon$, there exists a positive $\delta$ (depending only on $\varepsilon$) such that the following holds: If $p \geq \frac{1+\varepsilon}{k}$, then with probability tending to $1$ as $k \to \infty$, the random graph $G_p$ contains a cycle of length at least $n_{\mathcal{H}}(\delta k)$, where $n_\mathcal{H}(k)>k$ is the minimum number of vertices in an $\mathcal{H}$-free graph of average degree at least $k$. Thus in particular $G_p$ as above typically contains a cycle of length at least linear in $k$.

ANALISIS PERINGKAT TOP BRAND OJEK ONLINE MENGGUNAKAN JEJARING SOSIAL PERCAKAPAN TWITTER

2019 ◽  
Vol 24 (2) ◽  
pp. 88-104
Author(s):  
Ilham Aminudin ◽  
Dyah Anggraini
Keyword(s):  
Social Media ◽  
Social Network ◽  
Social Network Analysis ◽  
Network Analysis ◽  
Path Length ◽  
Average Path Length ◽  
Average Degree ◽  
Clustering Coefficient ◽  
R Programming

Banyak bisnis mulai muncul dengan melibatkan pengembangan teknologi internet. Salah satunya adalah bisnis di aplikasi berbasis penyedia layanan di bidang moda transportasi berbasis online yang ternyata dapat memberikan solusi dan menjawab berbagai kekhawatiran publik tentang layanan transportasi umum. Kemacetan lalu lintas di kota-kota besar dan ketegangan publik dengan keamanan transportasi umum diselesaikan dengan adanya aplikasi transportasi online seperti Grab dan Gojek yang memberikan kemudahan dan kenyamanan bagi penggunanya Penelitian ini dilakukan untuk menganalisa keaktifan percakapan brand jasa transportasi online di jejaring sosial Twitter berdasarkan properti jaringan. Penelitian dilakukan dengan dengan mengambil data dari percakapan pengguna di social media Twitter dengan cara crawling menggunakan Bahasa pemrograman R programming dan software R Studio dan pembuatan model jaringan dengan software Gephy. Setelah itu data dianalisis menggunakan metode social network analysis yang terdiri berdasarkan properti jaringan yaitu size, density, modularity, diameter, average degree, average path length, dan clustering coefficient dan nantinya hasil analisis akan dibandingkan dari setiap properti jaringan kedua brand jasa transportasi Online dan ditentukan strategi dalam meningkatkan dan mempertahankan keaktifan serta tingkat kehadiran brand jasa transportasi online, Grab dan Gojek.

scholarly journals RoboPol: AGN polarimetric monitoring data

2020 ◽  
Author(s):  
D Blinov ◽  
S Kiehlmann ◽  
V Pavlidou ◽  
G V Panopoulou ◽  
R Skalidis ◽  
...  
Keyword(s):  
Active Galactic Nuclei ◽  
Galactic Nuclei ◽  
Average Degree ◽  
Monitoring Data ◽  
Degree Of Polarization ◽  
Time Interval ◽  
Current Version ◽  
Variability Index ◽  
Entire Dataset

Abstract We present uniformly reprocessed and re-calibrated data from the RoboPol programme of optopolarimetric monitoring of active galactic nuclei (AGN), covering observations between 2013, when the instrument was commissioned, and 2017. In total, the dataset presented in this paper includes 5068 observations of 222 AGN with Dec > −25○. We describe the current version of the RoboPol pipeline that was used to process and calibrate the entire dataset, and we make the data publicly available for use by the astronomical community. Average quantities summarising optopolarimetric behaviour (average degree of polarization, polarization variability index) are also provided for each source we have observed and for the time interval we have followed it.

scholarly journals Centrality-friendship paradoxes: when our friends are more important than us

2018 ◽  
Vol 7 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Desmond J Higham
Keyword(s):  
Network Science ◽  
Sufficient Conditions ◽  
Sampling Bias ◽  
Average Degree ◽  
Science Literature ◽  
Eigenvector Centrality ◽  
General Matrix ◽  
Theoretical Support ◽  
The Social ◽  
Katz Centrality

Abstract The friendship paradox states that, on average, our friends have more friends than we do. In network terms, the average degree over the nodes can never exceed the average degree over the neighbours of nodes. This effect, which is a classic example of sampling bias, has attracted much attention in the social science and network science literature, with variations and extensions of the paradox being defined, tested and interpreted. Here, we show that a version of the paradox holds rigorously for eigenvector centrality: on average, our friends are more important than us. We then consider general matrix-function centrality, including Katz centrality, and give sufficient conditions for the paradox to hold. We also discuss which results can be generalized to the cases of directed and weighted edges. In this way, we add theoretical support for a field that has largely been evolving through empirical testing.

scholarly journals Friendship paradox in growth networks: analytical and empirical analysis

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Sergei P. Sidorov ◽  
Sergei V. Mironov ◽  
Alexey A. Grigoriev
Keyword(s):  
Real World ◽  
Preferential Attachment ◽  
Empirical Studies ◽  
Mean Field ◽  
Network Models ◽  
Average Degree ◽  
Closure Model ◽  
Triadic Closure ◽  
Attachment Mechanism ◽  
Over Time

AbstractMany empirical studies have shown that in social, citation, collaboration, and other types of networks in real world, the degree of almost every node is less than the average degree of its neighbors. This imbalance is well known in sociology as the friendship paradox and states that your friends are more popular than you on average. If we introduce a value equal to the ratio of the average degree of the neighbors for a certain node to the degree of this node (which is called the ‘friendship index’, FI), then the FI value of more than 1 for most nodes indicates the presence of the friendship paradox in the network. In this paper, we study the behavior of the FI over time for networks generated by growth network models. We will focus our analysis on two models based on the use of the preferential attachment mechanism: the Barabási–Albert model and the triadic closure model. Using the mean-field approach, we obtain differential equations describing the dynamics of changes in the FI over time, and accordingly, after obtaining their solutions, we find the expected values of this index over iterations. The results show that the values of FI are decreasing over time for all nodes in both models. However, for networks constructed in accordance with the triadic closure model, this decrease occurs at a much slower rate than for the Barabási–Albert graphs. In addition, we analyze several real-world networks and show that their FI distributions follow a power law. We show that both the Barabási–Albert and the triadic closure networks exhibit the same behavior. However, for networks based on the triadic closure model, the distributions of FI are more heavy-tailed and, in this sense, are closer to the distributions for real networks.

scholarly journals Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

Fibre medullation in Blackface lambs and hoggs

1958 ◽  
Vol 51 (3) ◽  
pp. 257-264 ◽  
Author(s):  
J. M. Pilkington ◽  
A. F. Purser
Keyword(s):  
Average Degree ◽  
Fibre Types ◽  
Total Variance ◽  
Weighted Mean ◽  
The Mean

A method has been described of assessing the average degree of medullation in fleece samples. This method combines information about the various fibre types and the proportion of each present in the sample, by assigning 100 fibres to classes with scores 1–5 according to the degree of medullation. A weighted mean score was determined, ten times this mean being defined as the ‘medullation index’. The index has been used for 2 years on samples taken from 2-month-old lambs and 14-month-old hoggs of the Blackface breed. Drawings of fibre types showed that the internal and external diameters and their ratio all increase with the score.The mean medullation index for the 2-month-old lambs in the 2 years was 25·6 and 24·8. The effects of sex and type of birth of lamb and age of dam were assessed by fitting constants, but their contribution to the total variance was very small. The regression of medullation on age of lamb when sampled was −0·11 units per day in both years, and was highly significant. Possible explanations for this decline of medullation are discussed.The mean medullation index for 14-month-old hoggs was 16·1 in both years. Estimate of correlation between lamb and hogg for the 2 years were + 0·45 and + 0·33. It is probable that variation in medullation within the fleece and in fibre shedding account for these low values.

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