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1

Additional Closeness and Networks Growth

Dangalchev Chavdar

Fundamenta Informaticae

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2020

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Vol. 176, nr 1

1--15

EN

Creation and growth are very important in network analysis. In this article we propose one possible model for networks generation. The probabilities of new links are proportional to the expected closeness of the added node. We also propose a new characteristic of graphs - additional closeness, which measures the maximal closeness of a graph after adding a new link. Some properties of the additional closeness are explored. Three different ways of joining two networks are investigated.

2

Networks with Extremal Closeness

Rupnik Poklukar Darja, Žerovnik Janez

Fundamenta Informaticae

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2019

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Vol. 167, nr 3

219--234

EN

Closeness is a measure of centrality, an important feature of communication and social networks. Extremal networks among all graphs and among several subclasses of graphs including trees and cacti are given. In addition, maximal graphs among cacti with fixed number of cycles and among cacti with given number of cut edges are provided.

3

Residual Closeness of Generalized Thorn Graphs

Dangalchev C.

Fundamenta Informaticae

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2018

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Vol. 162, nr 1

1--15

EN

One of the most sensitive characteristics of network vulnerability is residual closeness. Calculating the closeness and the residual closeness of larger graphs is a time consuming and operations heavy process. In this article, we try to mitigate the process for thorn graphs-we present the thorn graphs residual closeness as a function of the closeness and the residual closeness of the original graphs.

4

T-Rough Approximation Pairs and Covering Based Rough Sets

Zhang X., Zhang Y., Xue Z., Ma Y.

Fundamenta Informaticae

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2015

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Vol. 142, nr 1-4

195--212

EN

The relationships between T-rough sets and covering based rough sets are investigated, and two kinds of generated methods of rough approximation operators from existing rough sets are established. Moreover, applying the aforementioned generated methods of approximation operators, S-rough sets and some new covering-based rough sets are introduced and their basic properties are discussed.

5

Residual Closeness in Cycles and Related Networks

Odabaş Z. N., Aytaç A.

Fundamenta Informaticae

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2013

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Vol. 124, nr 3

297--307

EN

Networks are known to be prone to node or link failures. A central issue in the analysis of networks is the assessment of their stability and reliability. The main aim is to understand, predict, and possibly even control the behavior of a networked system under attacks or disfunctions of any type. A central concept that is used to assess stability and robustness of the performance of a network under failures is that of vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far. In this paper, we study the vulnerability of cycles and related graphs to the failure of individual vertices, using a measure called residual closeness which provides a more sensitive characterization of the graph than some other well-known vulnerability measures.

6

Possible Rough Ingredients of Concepts in Approximation Spaces

Gomolińska A.

Fundamenta Informaticae

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2006

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Vol. 72, nr 1-3

139-154

EN

We discuss the problem of rough ingredients and parts of concepts of an indiscernibility-based approximation space. The notion of a (rough) ingredient is extended to the notion of a possible (rough) ingredient, and analogously in the case of parts. The term "possible" means that a concept is perceived as a candidate for a future substitute of some ingredient. Our approach is in line with rough mereology except for allowing the empty concept for the sake of simplicity.