36,947 research outputs found
Strong, weak or no balance? Testing structural hypotheses in real heterogeneous networks
The abundance of data about social, economic and political relationships
allows social theories to be tested against empirical evidence and human
behaviour to be analyzed just as any other natural phenomenon. Here we focus on
balance theory, stating that actors in signed social networks tend to avoid the
formation of `unbalanced', or `frustrated', cycles, i.e. cycles with an odd
number of negative links. This statement can be supported statistically only
after a comparison with a null model. Since the existing benchmarks do not
typically account for the heterogeneity of individual actors, here we first
extend the Exponential Random Graphs framework to signed networks with both
global (homogeneous) and local (heterogeneous) constraints and then employ them
to assess the significance of unbalanced patterns in several real-world
networks. We find that the nature and level of balance in social networks
crucially depends on the null model employed. In particular, the study of
signed triangles and signed communities reveals that homogeneous null models
favour the weak version of balance theory, according to which only triangles
with one negative link should be under-represented in social networks, while
heterogeneous null models favour the strong version of balance theory,
according to which also triangles with all negative links should be
under-represented. Biological networks, instead, display almost inverted
patterns and strong frustration under any benchmark, confirming that structural
balance inherently distinguishes social networks from other signed networks.Comment: 33 pages, 11 figures, 4 table
Signed Networks in Social Media
Relations between users on social media sites often reflect a mixture of
positive (friendly) and negative (antagonistic) interactions. In contrast to
the bulk of research on social networks that has focused almost exclusively on
positive interpretations of links between people, we study how the interplay
between positive and negative relationships affects the structure of on-line
social networks. We connect our analyses to theories of signed networks from
social psychology. We find that the classical theory of structural balance
tends to capture certain common patterns of interaction, but that it is also at
odds with some of the fundamental phenomena we observe --- particularly related
to the evolving, directed nature of these on-line networks. We then develop an
alternate theory of status that better explains the observed edge signs and
provides insights into the underlying social mechanisms. Our work provides one
of the first large-scale evaluations of theories of signed networks using
on-line datasets, as well as providing a perspective for reasoning about social
media sites
Emergent Behaviors over Signed Random Networks in Dynamical Environments
We study asymptotic dynamical patterns that emerge among a set of nodes that
interact in a dynamically evolving signed random network. Node interactions
take place at random on a sequence of deterministic signed graphs. Each node
receives positive or negative recommendations from its neighbors depending on
the sign of the interaction arcs, and updates its state accordingly. Positive
recommendations follow the standard consensus update while two types of
negative recommendations, each modeling a different type of antagonistic or
malicious interaction, are considered. Nodes may weigh positive and negative
recommendations differently, and random processes are introduced to model the
time-varying attention that nodes pay to the positive and negative
recommendations. Various conditions for almost sure convergence, divergence,
and clustering of the node states are established. Some fundamental
similarities and differences are established for the two notions of negative
recommendations
Multirelational Organization of Large-scale Social Networks in an Online World
The capacity to collect fingerprints of individuals in online media has
revolutionized the way researchers explore human society. Social systems can be
seen as a non-linear superposition of a multitude of complex social networks,
where nodes represent individuals and links capture a variety of different
social relations. Much emphasis has been put on the network topology of social
interactions, however, the multi-dimensional nature of these interactions has
largely been ignored in empirical studies, mostly because of lack of data.
Here, for the first time, we analyze a complete, multi-relational, large social
network of a society consisting of the 300,000 odd players of a massive
multiplayer online game. We extract networks of six different types of
one-to-one interactions between the players. Three of them carry a positive
connotation (friendship, communication, trade), three a negative (enmity, armed
aggression, punishment). We first analyze these types of networks as separate
entities and find that negative interactions differ from positive interactions
by their lower reciprocity, weaker clustering and fatter-tail degree
distribution. We then proceed to explore how the inter-dependence of different
network types determines the organization of the social system. In particular
we study correlations and overlap between different types of links and
demonstrate the tendency of individuals to play different roles in different
networks. As a demonstration of the power of the approach we present the first
empirical large-scale verification of the long-standing structural balance
theory, by focusing on the specific multiplex network of friendship and enmity
relations.Comment: 7 pages, 5 figures, accepted for publication in PNA
The Evolution of Beliefs over Signed Social Networks
We study the evolution of opinions (or beliefs) over a social network modeled
as a signed graph. The sign attached to an edge in this graph characterizes
whether the corresponding individuals or end nodes are friends (positive links)
or enemies (negative links). Pairs of nodes are randomly selected to interact
over time, and when two nodes interact, each of them updates its opinion based
on the opinion of the other node and the sign of the corresponding link. This
model generalizes DeGroot model to account for negative links: when two enemies
interact, their opinions go in opposite directions. We provide conditions for
convergence and divergence in expectation, in mean-square, and in almost sure
sense, and exhibit phase transition phenomena for these notions of convergence
depending on the parameters of the opinion update model and on the structure of
the underlying graph. We establish a {\it no-survivor} theorem, stating that
the difference in opinions of any two nodes diverges whenever opinions in the
network diverge as a whole. We also prove a {\it live-or-die} lemma, indicating
that almost surely, the opinions either converge to an agreement or diverge.
Finally, we extend our analysis to cases where opinions have hard lower and
upper limits. In these cases, we study when and how opinions may become
asymptotically clustered to the belief boundaries, and highlight the crucial
influence of (strong or weak) structural balance of the underlying network on
this clustering phenomenon
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
Measuring social dynamics in a massive multiplayer online game
Quantification of human group-behavior has so far defied an empirical,
falsifiable approach. This is due to tremendous difficulties in data
acquisition of social systems. Massive multiplayer online games (MMOG) provide
a fascinating new way of observing hundreds of thousands of simultaneously
socially interacting individuals engaged in virtual economic activities. We
have compiled a data set consisting of practically all actions of all players
over a period of three years from a MMOG played by 300,000 people. This
large-scale data set of a socio-economic unit contains all social and economic
data from a single and coherent source. Players have to generate a virtual
income through economic activities to `survive' and are typically engaged in a
multitude of social activities offered within the game. Our analysis of
high-frequency log files focuses on three types of social networks, and tests a
series of social-dynamics hypotheses. In particular we study the structure and
dynamics of friend-, enemy- and communication networks. We find striking
differences in topological structure between positive (friend) and negative
(enemy) tie networks. All networks confirm the recently observed phenomenon of
network densification. We propose two approximate social laws in communication
networks, the first expressing betweenness centrality as the inverse square of
the overlap, the second relating communication strength to the cube of the
overlap. These empirical laws provide strong quantitative evidence for the Weak
ties hypothesis of Granovetter. Further, the analysis of triad significance
profiles validates well-established assertions from social balance theory. We
find overrepresentation (underrepresentation) of complete (incomplete) triads
in networks of positive ties, and vice versa for networks of negative ties...Comment: 23 pages 19 figure
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