Sergey Kirgizov

http://kirgizov.link/

Personal information

http://kirgizov.link/

Affiliation(s)

Laboratoire Electronique, Informatique et Image (Le2i). CNRS : UMR6306 - Université de Bourgogne - Arts et Métiers ParisTech
UFR Sciences et Techniques BP 47870 21078 Dijon cedex, France

Expertise

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Essay and Opinion

A new graph density

Deposited on 08 / 04 / 2015 Sergey Kirgizov

For a given graph $G$ we propose the non-classical definition of its true density: $\rho(G) = \mathcal{M}ass (G) / \mathcal{V}ol (G)$, where the $\mathcal{M}ass$ of the graph $G$ is a total mass of its links and nodes, and...

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Essay and Opinion

A new graph density

Deposited on 08 / 04 / 2015 Sergey Kirgizov

For a given graph $G$ we propose the non-classical definition of its true density: $\rho(G) = \mathcal{M}ass (G) / \mathcal{V}ol (G)$, where the $\mathcal{M}ass$ of the graph $G$ is a total mass of its links and nodes, and...

Read the article

1

1

On 2017 April 10 - Hello Michaël,
Indeed, you found a counterexample to the property IV. I should think a bit more about it, but the first idea that comes to mind is to propose not only the properties of graph volume, but also some properties about the new graph density, for example IV can be translated as:\[ \rho (G) \le \rho (G + v^1)\tag{IV about density}\]The new IV will work for your counterexample...

In A new graph density

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1

0

On 2015 December 30 - Well, it turns out that the volume defined in this note is just a geometric mean of eccent...

In A new graph density

READ IN CONTEXT

0

0

On 2015 April 21 - Well, even the modified property VI about densities does not work. Consider the following counterexample: $$\rho (\bullet - \bullet) = 3 \quad \ge \quad \rho (\bullet - \bullet - \bullet) = \sqrt{5} \approx 2...

In A new graph density

READ IN CONTEXT

Priority 18

Principles of the Self-Journal of Science: bringing ethics and freedom to scientific publishing

On 2015 January 24

Priority 1

A new graph density

On 2015 April 08

1

1

On 2017 April 10 - Hello Michaël,
Indeed, you found a counterexample to the property IV. I should think a bit more about it, but the first idea that comes to mind is to propose not only the properties of graph volume, but also some properties about the new graph density, for example IV can be translated as:\[ \rho (G) \le \rho (G + v^1)\tag{IV about density}\]The new IV will work for your counterexample...

In A new graph density

READ IN CONTEXT

1

0

On 2015 December 30 - Well, it turns out that the volume defined in this note is just a geometric mean of eccent...

In A new graph density

READ IN CONTEXT

0

0

On 2015 April 21 - Well, even the modified property VI about densities does not work. Consider the following counterexample: $$\rho (\bullet - \bullet) = 3 \quad \ge \quad \rho (\bullet - \bullet - \bullet) = \sqrt{5} \approx 2...

In A new graph density

READ IN CONTEXT

1

1

On 2017 April 10 - Hello Michaël,
Indeed, you found a counterexample to the property IV. I should think a bit more about it, but the first idea that comes to mind is to propose not only the properties of graph volume, but also some properties about the new graph density, for example IV can be translated as:\[ \rho (G) \le \rho (G + v^1)\tag{IV about density}\]The new IV will work for your counterexample...

In A new graph density

READ IN CONTEXT

0

0

On 2015 April 21 - Well, even the modified property VI about densities does not work. Consider the following counterexample: $$\rho (\bullet - \bullet) = 3 \quad \ge \quad \rho (\bullet - \bullet - \bullet) = \sqrt{5} \approx 2...

In A new graph density

READ IN CONTEXT

1

0

On 2015 December 30 - Well, it turns out that the volume defined in this note is just a geometric mean of eccent...

In A new graph density

READ IN CONTEXT

1

1

On 2017 April 10 - Hello Michaël,
Indeed, you found a counterexample to the property IV. I should think a bit more about it, but the first idea that comes to mind is to propose not only the properties of graph volume, but also some properties about the new graph density, for example IV can be translated as:\[ \rho (G) \le \rho (G + v^1)\tag{IV about density}\]The new IV will work for your counterexample...

In A new graph density

READ IN CONTEXT

1

0

On 2015 December 30 - Well, it turns out that the volume defined in this note is just a geometric mean of eccent...

In A new graph density

READ IN CONTEXT

0

0

On 2015 April 21 - Well, even the modified property VI about densities does not work. Consider the following counterexample: $$\rho (\bullet - \bullet) = 3 \quad \ge \quad \rho (\bullet - \bullet - \bullet) = \sqrt{5} \approx 2...

In A new graph density

READ IN CONTEXT