270 research outputs found
Probabilistic Inductive Classes of Graphs
Models of complex networks are generally defined as graph stochastic
processes in which edges and vertices are added or deleted over time to
simulate the evolution of networks. Here, we define a unifying framework -
probabilistic inductive classes of graphs - for formalizing and studying
evolution of complex networks. Our definition of probabilistic inductive class
of graphs (PICG) extends the standard notion of inductive class of graphs (ICG)
by imposing a probability space. A PICG is given by: (1) class B of initial
graphs, the basis of PICG, (2) class R of generating rules, each with
distinguished left element to which the rule is applied to obtain the right
element, (3) probability distribution specifying how the initial graph is
chosen from class B, (4) probability distribution specifying how the rules from
class R are applied, and, finally, (5) probability distribution specifying how
the left elements for every rule in class R are chosen. We point out that many
of the existing models of growing networks can be cast as PICGs. We present how
the well known model of growing networks - the preferential attachment model -
can be studied as PICG. As an illustration we present results regarding the
size, order, and degree sequence for PICG models of connected and 2-connected
graphs.Comment: 15 pages, 6 figure
Dynamics of Social Balance on Networks
We study the evolution of social networks that contain both friendly and
unfriendly pairwise links between individual nodes. The network is endowed with
dynamics in which the sense of a link in an imbalanced triad--a triangular loop
with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this
dynamics, an infinite network undergoes a dynamic phase transition from a
steady state to "paradise"--all links are friendly--as the propensity p for
friendly links in an update event passes through 1/2. A finite network always
falls into a socially-balanced absorbing state where no imbalanced triads
remain. If the additional constraint that the number of imbalanced triads in
the network does not increase in an update is imposed, then the network quickly
reaches a balanced final state.Comment: 10 pages, 7 figures, 2-column revtex4 forma
Visualizing Structural Balance in Signed Networks
Network visualization has established as a key complement to network analysis
since the large variety of existing network layouts are able to graphically
highlight different properties of networks. However, signed networks, i.e.,
networks whose edges are labeled as friendly (positive) or antagonistic
(negative), are target of few of such layouts and none, to our knowledge, is
able to show structural balance, i.e., the tendency of cycles towards including
an even number of negative edges, which is a well-known theory for studying
friction and polarization.
In this work we present Structural-balance-viz: a novel visualization method
showing whether a connected signed network is balanced or not and, in the
latter case, how close the network is to be balanced. Structural-balance-viz
exploits spectral computations of the signed Laplacian matrix to place
network's nodes in a Cartesian coordinate system resembling a balance (a
scale). Moreover, it uses edge coloring and bundling to distinguish positive
and negative interactions. The proposed visualization method has
characteristics desirable in a variety of network analysis tasks:
Structural-balance-viz is able to provide indications of balance/polarization
of the whole network and of each node, to identify two factions of nodes on the
basis of their polarization, and to show their cumulative characteristics.
Moreover, the layout is reproducible and easy to compare.
Structural-balance-viz is validated over synthetic-generated networks and
applied to a real-world dataset about political debates confirming that it is
able to provide meaningful interpretations
The interplay of microscopic and mesoscopic structure in complex networks
Not all nodes in a network are created equal. Differences and similarities
exist at both individual node and group levels. Disentangling single node from
group properties is crucial for network modeling and structural inference.
Based on unbiased generative probabilistic exponential random graph models and
employing distributive message passing techniques, we present an efficient
algorithm that allows one to separate the contributions of individual nodes and
groups of nodes to the network structure. This leads to improved detection
accuracy of latent class structure in real world data sets compared to models
that focus on group structure alone. Furthermore, the inclusion of hitherto
neglected group specific effects in models used to assess the statistical
significance of small subgraph (motif) distributions in networks may be
sufficient to explain most of the observed statistics. We show the predictive
power of such generative models in forecasting putative gene-disease
associations in the Online Mendelian Inheritance in Man (OMIM) database. The
approach is suitable for both directed and undirected uni-partite as well as
for bipartite networks
The Citation Field of Evolutionary Economics
Evolutionary economics has developed into an academic field of its own,
institutionalized around, amongst others, the Journal of Evolutionary Economics
(JEE). This paper analyzes the way and extent to which evolutionary economics
has become an interdisciplinary journal, as its aim was: a journal that is
indispensable in the exchange of expert knowledge on topics and using
approaches that relate naturally with it. Analyzing citation data for the
relevant academic field for the Journal of Evolutionary Economics, we use
insights from scientometrics and social network analysis to find that, indeed,
the JEE is a central player in this interdisciplinary field aiming mostly at
understanding technological and regional dynamics. It does not, however, link
firmly with the natural sciences (including biology) nor to management
sciences, entrepreneurship, and organization studies. Another journal that
could be perceived to have evolutionary acumen, the Journal of Economic Issues,
does relate to heterodox economics journals and is relatively more involved in
discussing issues of firm and industry organization. The JEE seems most keen to
develop theoretical insights
Dynamics of MOOC Discussion Forums
In this integrated study of dynamics in MOOCs discussion forums, we analyze the interplay of temporal patterns, discussion content, and the social structure emerging from the communication using mixed methods. A special focus is on the yet under-explored aspect of time dynamics and influence of the course structure on forum participation. Our analyses show dependencies between the course structure (video opening time and assignment deadlines) and the overall forum activity whereas such a clear link could only be partially observed considering the discussion content. For analyzing the social dimension we apply role modeling techniques from social network analysis. While the types of user roles based on connection patterns are relatively stable over time, the high fluctuation of active contributors lead to frequent changes from active to passive roles during the course. However, while most users do not create many social connections they can play an important role in the content dimension triggering discussions on the course subject. Finally, we show that forum activity level can be predicted one week in advance based on the course structure, forum activity history and attributes of the communication network which enables identification of periods when increased tutor supports in the forum is necessary
Detecting groups of similar components in complex networks
We study how to detect groups in a complex network each of which consists of
component nodes sharing a similar connection pattern. Based on the mixture
models and the exploratory analysis set up by Newman and Leicht (Newman and
Leicht 2007 {\it Proc. Natl. Acad. Sci. USA} {\bf 104} 9564), we develop an
algorithm that is applicable to a network with any degree distribution. The
partition of a network suggested by this algorithm also applies to its
complementary network. In general, groups of similar components are not
necessarily identical with the communities in a community network; thus
partitioning a network into groups of similar components provides additional
information of the network structure. The proposed algorithm can also be used
for community detection when the groups and the communities overlap. By
introducing a tunable parameter that controls the involved effects of the
heterogeneity, we can also investigate conveniently how the group structure can
be coupled with the heterogeneity characteristics. In particular, an
interesting example shows a group partition can evolve into a community
partition in some situations when the involved heterogeneity effects are tuned.
The extension of this algorithm to weighted networks is discussed as well.Comment: 14 pages, 10 figures, latex, more discussions added, typos cleare
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