441 research outputs found
Direct blockmodeling of valued and binary networks: a dichotomization-free approach
A long-standing open problem with direct blockmodeling is that it is
explicitly intended for binary, not valued, networks. The underlying dilemma is
how empirical valued blocks can be compared with ideal binary blocks, an
intrinsic problem in the direct approach where partitions are solely determined
through such comparisons. Addressing this dilemma, valued networks have either
been dichotomized into binary versions, or novel types of ideal valued blocks
have been introduced. Both these workarounds are problematic in terms of
interpretability, unwanted data reduction, and the often arbitrary setting of
model parameters.
This paper proposes a direct blockmodeling approach that effectively bypasses
the dilemma with blockmodeling of valued networks. By introducing an adaptive
weighted correlation-based criteria function, the proposed approach is directly
applicable to both binary and valued networks, without any form of
dichotomization or transformation of the valued (or binary) data at any point
in the analysis, while still using the conventional set of ideal binary blocks
from structural, regular and generalized blockmodeling.
The approach is demonstrated by structural, regular and generalized
blockmodeling applications of six classical binary and valued networks. Finding
feasible and intuitive optimal solutions in both the binary and valued
examples, the approach is proposed not only as a practical,
dichotomization-free heuristic for blockmodeling of valued networks but also,
through its additional benefits, as an alternative to the conventional direct
approach to blockmodeling
Generating global network structures by triad types
This paper addresses the question of whether it is possible to generate
networks with a given global structure (defined by selected blockmodels, i.e.,
cohesive, core-periphery, hierarchical and transitivity), considering only
different types of triads. Two methods are used to generate networks: (i) the
method of relocating links; and (ii) the Monte Carlo Multi Chain algorithm
implemented in the "ergm" package implemented in R. Although all types of
triads can generate networks with the selected blockmodel types, the selection
of only a subset of triads improves the generated networks' blockmodel
structure. However, in the case of a hierarchical blockmodel without complete
blocks on the diagonal, additional local structures are needed to achieve the
desired global structure of generated networks. This shows that blockmodels can
emerge based on only local processes that do not take attributes into account
Generalized Blockmodeling with Pajek
Abstract One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. Batagelj, Doreian, and Ferligoj developed a generalized approach to blockmodeling and methods where a set of observed relations are fitted to a pre-specified blockmodel. In the paper this generalized blockmodeling approach as implemented in program Pajek is described. An overview of the blockmodeling procedures in Pajek is given and is illustrated by some examples
A Triclustering Approach for Time Evolving Graphs
This paper introduces a novel technique to track structures in time evolving
graphs. The method is based on a parameter free approach for three-dimensional
co-clustering of the source vertices, the target vertices and the time. All
these features are simultaneously segmented in order to build time segments and
clusters of vertices whose edge distributions are similar and evolve in the
same way over the time segments. The main novelty of this approach lies in that
the time segments are directly inferred from the evolution of the edge
distribution between the vertices, thus not requiring the user to make an a
priori discretization. Experiments conducted on a synthetic dataset illustrate
the good behaviour of the technique, and a study of a real-life dataset shows
the potential of the proposed approach for exploratory data analysis
Role models for complex networks
We present a framework for automatically decomposing ("block-modeling") the
functional classes of agents within a complex network. These classes are
represented by the nodes of an image graph ("block model") depicting the main
patterns of connectivity and thus functional roles in the network. Using a
first principles approach, we derive a measure for the fit of a network to any
given image graph allowing objective hypothesis testing. From the properties of
an optimal fit, we derive how to find the best fitting image graph directly
from the network and present a criterion to avoid overfitting. The method can
handle both two-mode and one-mode data, directed and undirected as well as
weighted networks and allows for different types of links to be dealt with
simultaneously. It is non-parametric and computationally efficient. The
concepts of structural equivalence and modularity are found as special cases of
our approach. We apply our method to the world trade network and analyze the
roles individual countries play in the global economy
Generalized Blockmodeling of Multi-Valued Networks
This research presents an extension to generalized blockmodeling where there are more than two types of objects to be clustered based on valued network data. We use the ideas in homogeneity blockmodeling to develop an optimization model to perform the clustering of the objects and the resulting partitioning of the ties so as to minimize the inconsistency of an empirical block with an ideal block. The ideal block types used in this modeling are null (all zeros), complete (all ones) and valued. Two case studies are presented: the Southern Women dataset and a larger example using a subset of the IMDb movie dataset
Clustering and Community Detection in Directed Networks: A Survey
Networks (or graphs) appear as dominant structures in diverse domains,
including sociology, biology, neuroscience and computer science. In most of the
aforementioned cases graphs are directed - in the sense that there is
directionality on the edges, making the semantics of the edges non symmetric.
An interesting feature that real networks present is the clustering or
community structure property, under which the graph topology is organized into
modules commonly called communities or clusters. The essence here is that nodes
of the same community are highly similar while on the contrary, nodes across
communities present low similarity. Revealing the underlying community
structure of directed complex networks has become a crucial and
interdisciplinary topic with a plethora of applications. Therefore, naturally
there is a recent wealth of research production in the area of mining directed
graphs - with clustering being the primary method and tool for community
detection and evaluation. The goal of this paper is to offer an in-depth review
of the methods presented so far for clustering directed networks along with the
relevant necessary methodological background and also related applications. The
survey commences by offering a concise review of the fundamental concepts and
methodological base on which graph clustering algorithms capitalize on. Then we
present the relevant work along two orthogonal classifications. The first one
is mostly concerned with the methodological principles of the clustering
algorithms, while the second one approaches the methods from the viewpoint
regarding the properties of a good cluster in a directed network. Further, we
present methods and metrics for evaluating graph clustering results,
demonstrate interesting application domains and provide promising future
research directions.Comment: 86 pages, 17 figures. Physics Reports Journal (To Appear
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