13,545 research outputs found
Active influence in dynamical models of structural balance in social networks
We consider a nonlinear dynamical system on a signed graph, which can be
interpreted as a mathematical model of social networks in which the links can
have both positive and negative connotations. In accordance with a concept from
social psychology called structural balance, the negative links play a key role
in both the structure and dynamics of the network. Recent research has shown
that in a nonlinear dynamical system modeling the time evolution of
"friendliness levels" in the network, two opposing factions emerge from almost
any initial condition. Here we study active external influence in this
dynamical model and show that any agent in the network can achieve any desired
structurally balanced state from any initial condition by perturbing its own
local friendliness levels. Based on this result, we also introduce a new
network centrality measure for signed networks. The results are illustrated in
an international relations network using United Nations voting record data from
1946 to 2008 to estimate friendliness levels amongst various countries.Comment: 7 pages, 3 figures, to appear in Europhysics Letters
(http://www.epletters.net
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
Coupled dynamics of node and link states in complex networks: A model for language competition
Inspired by language competition processes, we present a model of coupled
evolution of node and link states. In particular, we focus on the interplay
between the use of a language and the preference or attitude of the speakers
towards it, which we model, respectively, as a property of the interactions
between speakers (a link state) and as a property of the speakers themselves (a
node state). Furthermore, we restrict our attention to the case of two socially
equivalent languages and to socially inspired network topologies based on a
mechanism of triadic closure. As opposed to most of the previous literature,
where language extinction is an inevitable outcome of the dynamics, we find a
broad range of possible asymptotic configurations, which we classify as: frozen
extinction states, frozen coexistence states, and dynamically trapped
coexistence states. Moreover, metastable coexistence states with very long
survival times and displaying a non-trivial dynamics are found to be abundant.
Interestingly, a system size scaling analysis shows, on the one hand, that the
probability of language extinction vanishes exponentially for increasing system
sizes and, on the other hand, that the time scale of survival of the
non-trivial dynamical metastable states increases linearly with the size of the
system. Thus, non-trivial dynamical coexistence is the only possible outcome
for large enough systems. Finally, we show how this coexistence is
characterized by one of the languages becoming clearly predominant while the
other one becomes increasingly confined to "ghetto-like" structures: small
groups of bilingual speakers arranged in triangles, with a strong preference
for the minority language, and using it for their intra-group interactions
while they switch to the predominant language for communications with the rest
of the population.Comment: 21 pages, 15 figure
Social Stability and Extended Social Balance - Quantifying the Role of Inactive Links in Social Networks
Structural balance in social network theory starts from signed networks with
active relationships (friendly or hostile) to establish a hierarchy between
four different types of triadic relationships. The lack of an active link also
provides information about the network. To exploit the information that remains
uncovered by structural balance, we introduce the inactive relationship that
accounts for both neutral and nonexistent ties between two agents. This
addition results in ten types of triads, with the advantage that the network
analysis can be done with complete networks. To each type of triadic
relationship, we assign an energy that is a measure for its average occupation
probability. Finite temperatures account for a persistent form of disorder in
the formation of the triadic relationships. We propose a Hamiltonian with three
interaction terms and a chemical potential (capturing the cost of edge
activation) as an underlying model for the triadic energy levels. Our model is
suitable for empirical analysis of political networks and allows to uncover
generative mechanisms. It is tested on an extended data set for the standings
between two classes of alliances in a massively multi-player on-line game
(MMOG) and on real-world data for the relationships between countries during
the Cold War era. We find emergent properties in the triadic relationships
between the nodes in a political network. For example, we observe a persistent
hierarchy between the ten triadic energy levels across time and networks. In
addition, the analysis reveals consistency in the extracted model parameters
and a universal data collapse of a derived combination of global properties of
the networks. We illustrate that the model has predictive power for the
transition probabilities between the different triadic states.Comment: 21 pages, 10 figure
From sparse to dense and from assortative to disassortative in online social networks
Inspired by the analysis of several empirical online social networks, we
propose a simple reaction-diffusion-like coevolving model, in which individuals
are activated to create links based on their states, influenced by local
dynamics and their own intention. It is shown that the model can reproduce the
remarkable properties observed in empirical online social networks; in
particular, the assortative coefficients are neutral or negative, and the power
law exponents are smaller than 2. Moreover, we demonstrate that, under
appropriate conditions, the model network naturally makes transition(s) from
assortative to disassortative, and from sparse to dense in their
characteristics. The model is useful in understanding the formation and
evolution of online social networks.Comment: 10 pages, 7 figures and 2 table
Recommended from our members
Structural balance emerges and explains performance in risky decision-making.
Polarization affects many forms of social organization. A key issue focuses on which affective relationships are prone to change and how their change relates to performance. In this study, we analyze a financial institutional over a two-year period that employed 66 day traders, focusing on links between changes in affective relations and trading performance. Traders' affective relations were inferred from their IMs (>2 million messages) and trading performance was measured from profit and loss statements (>1 million trades). Here, we find that triads of relationships, the building blocks of larger social structures, have a propensity towards affective balance, but one unbalanced configuration resists change. Further, balance is positively related to performance. Traders with balanced networks have the "hot hand", showing streaks of high performance. Research implications focus on how changes in polarization relate to performance and polarized states can depolarize
Evolution of the digital society reveals balance between viral and mass media influence
Online social networks (OSNs) enable researchers to study the social universe
at a previously unattainable scale. The worldwide impact and the necessity to
sustain their rapid growth emphasize the importance to unravel the laws
governing their evolution. We present a quantitative two-parameter model which
reproduces the entire topological evolution of a quasi-isolated OSN with
unprecedented precision from the birth of the network. This allows us to
precisely gauge the fundamental macroscopic and microscopic mechanisms
involved. Our findings suggest that the coupling between the real pre-existing
underlying social structure, a viral spreading mechanism, and mass media
influence govern the evolution of OSNs. The empirical validation of our model,
on a macroscopic scale, reveals that virality is four to five times stronger
than mass media influence and, on a microscopic scale, individuals have a
higher subscription probability if invited by weaker social contacts, in
agreement with the "strength of weak ties" paradigm
Perspective: network-guided pattern formation of neural dynamics
The understanding of neural activity patterns is fundamentally linked to an
understanding of how the brain's network architecture shapes dynamical
processes. Established approaches rely mostly on deviations of a given network
from certain classes of random graphs. Hypotheses about the supposed role of
prominent topological features (for instance, the roles of modularity, network
motifs, or hierarchical network organization) are derived from these
deviations. An alternative strategy could be to study deviations of network
architectures from regular graphs (rings, lattices) and consider the
implications of such deviations for self-organized dynamic patterns on the
network. Following this strategy, we draw on the theory of spatiotemporal
pattern formation and propose a novel perspective for analyzing dynamics on
networks, by evaluating how the self-organized dynamics are confined by network
architecture to a small set of permissible collective states. In particular, we
discuss the role of prominent topological features of brain connectivity, such
as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the
notion of network-guided pattern formation with numerical simulations and
outline how it can facilitate the understanding of neural dynamics
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