3,099 research outputs found
Using adjacency matrices to lay out larger small-world networks
Many networks exhibit small-world properties. The structure of a small-world network is characterized by short average path lengths and high clustering coefficients. Few graph layout methods capture this structure well which limits their effectiveness and the utility of the visualization itself. Here we present an extension to our novel graphTPP layout method for laying out small-world networks using only their topological properties rather than their node attributes. The Watts–Strogatz model is used to generate a variety of graphs with a small-world network structure. Community detection algorithms are used to generate six different clusterings of the data. These clusterings, the adjacency matrix and edgelist are loaded into graphTPP and, through user interaction combined with linear projections of the adjacency matrix, graphTPP is able to produce a layout which visually separates these clusters. These layouts are compared to the layouts of two force-based techniques. graphTPP is able to clearly separate each of the communities into a spatially distinct area and the edge relationships between the clusters show the strength of their relationship. As a secondary contribution, an edge-grouping algorithm for graphTPP is demonstrated as a means to reduce visual clutter in the layout and reinforce the display of the strength of the relationship between two communities
Network Analysis with the Enron Email Corpus
We use the Enron email corpus to study relationships in a network by applying
six different measures of centrality. Our results came out of an in-semester
undergraduate research seminar. The Enron corpus is well suited to statistical
analyses at all levels of undergraduate education. Through this note's focus on
centrality, students can explore the dependence of statistical models on
initial assumptions and the interplay between centrality measures and
hierarchical ranking, and they can use completed studies as springboards for
future research. The Enron corpus also presents opportunities for research into
many other areas of analysis, including social networks, clustering, and
natural language processing.Comment: in Journal of Statistics Education, Volume 23, Number 2, 201
Community detection in temporal multilayer networks, with an application to correlation networks
Networks are a convenient way to represent complex systems of interacting
entities. Many networks contain "communities" of nodes that are more densely
connected to each other than to nodes in the rest of the network. In this
paper, we investigate the detection of communities in temporal networks
represented as multilayer networks. As a focal example, we study time-dependent
financial-asset correlation networks. We first argue that the use of the
"modularity" quality function---which is defined by comparing edge weights in
an observed network to expected edge weights in a "null network"---is
application-dependent. We differentiate between "null networks" and "null
models" in our discussion of modularity maximization, and we highlight that the
same null network can correspond to different null models. We then investigate
a multilayer modularity-maximization problem to identify communities in
temporal networks. Our multilayer analysis only depends on the form of the
maximization problem and not on the specific quality function that one chooses.
We introduce a diagnostic to measure \emph{persistence} of community structure
in a multilayer network partition. We prove several results that describe how
the multilayer maximization problem measures a trade-off between static
community structure within layers and larger values of persistence across
layers. We also discuss some computational issues that the popular "Louvain"
heuristic faces with temporal multilayer networks and suggest ways to mitigate
them.Comment: 42 pages, many figures, final accepted version before typesettin
Mathematical Formulation of Multi-Layer Networks
A network representation is useful for describing the structure of a large
variety of complex systems. However, most real and engineered systems have
multiple subsystems and layers of connectivity, and the data produced by such
systems is very rich. Achieving a deep understanding of such systems
necessitates generalizing "traditional" network theory, and the newfound deluge
of data now makes it possible to test increasingly general frameworks for the
study of networks. In particular, although adjacency matrices are useful to
describe traditional single-layer networks, such a representation is
insufficient for the analysis and description of multiplex and time-dependent
networks. One must therefore develop a more general mathematical framework to
cope with the challenges posed by multi-layer complex systems. In this paper,
we introduce a tensorial framework to study multi-layer networks, and we
discuss the generalization of several important network descriptors and
dynamical processes --including degree centrality, clustering coefficients,
eigenvector centrality, modularity, Von Neumann entropy, and diffusion-- for
this framework. We examine the impact of different choices in constructing
these generalizations, and we illustrate how to obtain known results for the
special cases of single-layer and multiplex networks. Our tensorial approach
will be helpful for tackling pressing problems in multi-layer complex systems,
such as inferring who is influencing whom (and by which media) in multichannel
social networks and developing routing techniques for multimodal transportation
systems.Comment: 15 pages, 5 figure
Uncovering nodes that spread information between communities in social networks
From many datasets gathered in online social networks, well defined community
structures have been observed. A large number of users participate in these
networks and the size of the resulting graphs poses computational challenges.
There is a particular demand in identifying the nodes responsible for
information flow between communities; for example, in temporal Twitter networks
edges between communities play a key role in propagating spikes of activity
when the connectivity between communities is sparse and few edges exist between
different clusters of nodes. The new algorithm proposed here is aimed at
revealing these key connections by measuring a node's vicinity to nodes of
another community. We look at the nodes which have edges in more than one
community and the locality of nodes around them which influence the information
received and broadcasted to them. The method relies on independent random walks
of a chosen fixed number of steps, originating from nodes with edges in more
than one community. For the large networks that we have in mind, existing
measures such as betweenness centrality are difficult to compute, even with
recent methods that approximate the large number of operations required. We
therefore design an algorithm that scales up to the demand of current big data
requirements and has the ability to harness parallel processing capabilities.
The new algorithm is illustrated on synthetic data, where results can be judged
carefully, and also on a real, large scale Twitter activity data, where new
insights can be gained
A theory on power in networks
The eigenvector centrality equation is a successful
compromise between simplicity and expressivity. It claims that central actors
are those connected with central others. For at least 70 years, this equation
has been explored in disparate contexts, including econometrics, sociometry,
bibliometrics, Web information retrieval, and network science. We propose an
equally elegant counterpart: the power equation , where
is the vector whose entries are the reciprocal of those of . It
asserts that power is in the hands of those connected with powerless others. It
is meaningful, for instance, in bargaining situations, where it is advantageous
to be connected to those who have few options. We tell the parallel, mostly
unexplored story of this intriguing equation
- …