ISSN 0005-1179, Automation and Remote Control, 2018, Vol. 79, No. 3, pp. 545–553.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
D.A. Gubanov, A.G. Chkhartishvili, 2016, published in Problemy Upravleniya, 2016, No. 6, pp. 12–17.
Inﬂuence Levels of Users and Meta-Users
of a Social Network
D. A. Gubanov
and A. G. Chkhartishvili
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Received June 17, 2016
Abstract—This paper considers an extension of the actional model of inﬂuence in online social
networks. Within the framework of this model, the inﬂuence and inﬂuence levels of separate
agents (users) and meta-agents (subsets of users) are calculated on the basis of their actions
taking into account the goals of a control subject (a Principal). We study some properties of
the inﬂuence function. An example illustrates how the actional model can be used to calculate
the inﬂuence levels of users in a concrete social network under available initial data.
Keywords: social network, the actional model of inﬂuence, inﬂuence level, meta-agent
Over the recent decade, the role of online social networks (Facebook, Twitter, etc.) in the life
of society has been growing appreciably. They are an informational reﬂection of a social network—
a structure consisting of a set of agents (users, communities and groups) and diﬀerent relations
between them (acquaintance, friendship, exchange of information, and so on).
An important aspect of informational and analytic work with social networks consists in es-
timating the inﬂuence level of users; see the paper  for associated problems. As a matter of
fact, inﬂuential users (also called public opinion leaders) to large extent predetermine the topics
and news for discussion as well as the positive or negative attitude to certain events or persons.
Therefore, inﬂuence level calculation is of theoretical and practical interest. There exist several ap-
proaches in this ﬁeld of research. Most investigations employ the structural approach to inﬂuence
estimation, which operates the notion of structural centrality from the classical theory of social
network analysis (SNA).
Starting from the 1950s, scientists have been developing and studying diﬀerent centrality indexes
such as node closeness, node degree, edge betweenness and others; for example, see the books [2, 3]
and the papers [4, 5] that more or less characterize inﬂuence. However, informational interaction
in a network is not always conditioned by its structure , which forms a serious drawback of the
Owing to the considerable advances in big data processing technologies, another (“computa-
tional”) approach is also being developed. According to this approach, the inﬂuence levels of users
in online social networks are often calculated using the modiﬁed versions of web page ranking
methods and scientometric methods [7–9]. The attempts to consider certain aspects of inﬂuence
(in particular, thematic inﬂuence or user activity) are fragmentary and unsystematic, which leads
to the same disadvantages as in the case of the structural approach.
Another large ﬁeld of research deals with the modeling of diﬀerent informational processes in
social networks. It is assumed that inﬂuence predetermines the dynamics of informational processes