Abstract
This paper presents the idea of measuring the formal impact of elements of a communication graph structure consisting of nodes and arcs on its entirety or subparts. Arcs and nodes, depending on the context, can be assigned different interpretations. E.g. in game theory its nodes may represent the players, often referred to as policy makers and arcs symbolize the relationships between them. In another context, however, nodes and arcs of the graph represent elements of technical infrastructure, e.g. a computer. The graph representing the tested relationships is called the communication graph and the influence of the elements on the entire graph (or its subpart) is referred to as power of the element. Taking into account the power of nodes and connections creates so-called incidence-power matrix more completely than the one formerly describing the communication graph.
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Notes
- 1.
It could be for example: traditional mail, e-mail, phone calls, personal meeting, etc. In such a case connections' weights can be modified by adding for example different values for to differentiate connections (and different weights of nodes).
- 2.
As we will see later, this condition is not necessary for games with graph representing communication between players.
- 3.
In Turnovec et al. (2008) one can find introduction of power indices without games theory but based on concept of permutations and their probability.
- 4.
We use the | . | operator to denote the cardinality of a finite set.
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Mercik, J. (2016). Formal a Priori Power Analysis of Elements of a Communication Graph. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, TP. (eds) Intelligent Information and Database Systems. ACIIDS 2016. Lecture Notes in Computer Science(), vol 9621. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49381-6_39
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