21 research outputs found
Portraits of Complex Networks
We propose a method for characterizing large complex networks by introducing
a new matrix structure, unique for a given network, which encodes structural
information; provides useful visualization, even for very large networks; and
allows for rigorous statistical comparison between networks. Dynamic processes
such as percolation can be visualized using animations. Applications to graph
theory are discussed, as are generalizations to weighted networks, real-world
network similarity testing, and applicability to the graph isomorphism problem.Comment: 6 pages, 9 figure
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
A network-specific approach to percolation in networks with bidirectional links
Methods for determining the percolation threshold usually study the behavior
of network ensembles and are often restricted to a particular type of
probabilistic node/link removal strategy. We propose a network-specific method
to determine the connectivity of nodes below the percolation threshold and
offer an estimate to the percolation threshold in networks with bidirectional
links. Our analysis does not require the assumption that a network belongs to a
specific ensemble and can at the same time easily handle arbitrary removal
strategies (previously an open problem for undirected networks). In validating
our analysis, we find that it predicts the effects of many known complex
structures (e.g., degree correlations) and may be used to study both
probabilistic and deterministic attacks.Comment: 6 pages, 8 figure
Furoku 4: Pajek 1.21 eno appu de-to
Translation of title: Appendix 4: Update to Pajek 1.21 Since the publication of this book, Pajek software has been expanded. Additions and changes are listed in the history document (history.htm) that is shown when Pajek is being installed. Most of the changes are self-explanatory or very specialized. Concise explanations are provided in the manual (PajekMan.pdf) which is constantly being updated. The manual can be downloaded from the Pajek website. Some changes, however, are quite fundamental and expand the applications of Pajek considerably even to novice users. In this Appendix, we briefly describe these changes
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Anthropology: Analyzing large kinship and marriage networks with Pgraph and Pajek
Five key problems of kinship networks are boundedness, cohesion, size and cohesive relinking, types of relations and relinking, and groups or roles. Approaches to solving these problems include formats available for electronic storage of genealogical data and representations of genealogies using graphs. P-graphs represent couples and uncoupled children as vertices, whereas parent-child links are the arcs connecting nodes both within and between different nuclear families. Using results from graph theory, P-graphs are shown to lend themselves to solutions of the problems discussed. Relinking of families through marriage, for example, can be formally defined as sets of bounded groups that are the cohesive cores of kinship networks, with nodes at various distances from such cores. The structure of such cores yields an analytic decomposition of kinship networks and constituent group and role relationships. The Pgraph and Pajek programs for large network analysis help both to represent kinship networks and their patterns and to solve problems of analysis
Exploratory social network analysis with Pajek. - 2nd ed.
This is an extensively revised and expanded second edition of the successful textbook on social network analysis integrating theory, applications, and network analysis using Pajek. The main structural concepts and their applications in social research are introduced with exercises. Pajek software and data sets are available so readers can learn network analysis through application and case studies. Readers will have the knowledge, skill, and tools to apply social network analysis across the social sciences, from anthropology and sociology to business administration and history. This second edition has a new chapter on random network models, for example, scale-free and small-world networks and Monte Carlo simulation; discussion of multiple relations, islands, and matrix multiplication; new structural indices such as eigenvector centrality, degree distribution, and clustering coefficients; new visualization options that include circular layout for partitions and drawing a network geographically as a 3D surface; and using Unicode labels. This new edition also includes instructions on exporting data from Pajek to R software. It offers updated descriptions and screen shots for working with Pajek (version 2.03)