657 research outputs found
Quantifying Triadic Closure in Multi-Edge Social Networks
Multi-edge networks capture repeated interactions between individuals. In
social networks, such edges often form closed triangles, or triads. Standard
approaches to measure this triadic closure, however, fail for multi-edge
networks, because they do not consider that triads can be formed by edges of
different multiplicity. We propose a novel measure of triadic closure for
multi-edge networks of social interactions based on a shared partner statistic.
We demonstrate that our operalization is able to detect meaningful closure in
synthetic and empirical multi-edge networks, where common approaches fail. This
is a cornerstone in driving inferential network analyses from the analysis of
binary networks towards the analyses of multi-edge and weighted networks, which
offer a more realistic representation of social interactions and relations.Comment: 19 pages, 5 figures, 6 table
Clustering in complex networks. I. General formalism
We develop a full theoretical approach to clustering in complex networks. A
key concept is introduced, the edge multiplicity, that measures the number of
triangles passing through an edge. This quantity extends the clustering
coefficient in that it involves the properties of two --and not just one--
vertices. The formalism is completed with the definition of a three-vertex
correlation function, which is the fundamental quantity describing the
properties of clustered networks. The formalism suggests new metrics that are
able to thoroughly characterize transitive relations. A rigorous analysis of
several real networks, which makes use of the new formalism and the new
metrics, is also provided. It is also found that clustered networks can be
classified into two main groups: the {\it weak} and the {\it strong
transitivity} classes. In the first class, edge multiplicity is small, with
triangles being disjoint. In the second class, edge multiplicity is high and so
triangles share many edges. As we shall see in the following paper, the class a
network belongs to has strong implications in its percolation properties
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
Topics in social network analysis and network science
This chapter introduces statistical methods used in the analysis of social
networks and in the rapidly evolving parallel-field of network science.
Although several instances of social network analysis in health services
research have appeared recently, the majority involve only the most basic
methods and thus scratch the surface of what might be accomplished.
Cutting-edge methods using relevant examples and illustrations in health
services research are provided
Node-Centric Detection of Overlapping Communities in Social Networks
We present NECTAR, a community detection algorithm that generalizes Louvain
method's local search heuristic for overlapping community structures. NECTAR
chooses dynamically which objective function to optimize based on the network
on which it is invoked. Our experimental evaluation on both synthetic benchmark
graphs and real-world networks, based on ground-truth communities, shows that
NECTAR provides excellent results as compared with state of the art community
detection algorithms
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
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