MultiNet: An interactive program for analysing and visualizing complex networks

MultiNet is a Windows-based computer program designed for exploratory data analysis of social and other networks. MultiNet is highly interactive and always provides both textual and visual representations of results. The visualizations are innovative in the use of colour and interaction, and some are unique to MultiNet. MultiNet was designed from the beginning to handle large amounts of data, and uses compact data formats, special storage schemes, and calculation methods that are highly efficient in terms of both space and time. MultiNet was also designed to handle large numbers of variables, both attribute (node) and network (link); it allows easy construction of new variables of either type by means of various operations on existing ones. Hybrid variables are easily constructed: node variables derived fiom networks; link variables derived fiom attributes. These capabilities provide crucial links among other parts of the program. The application of spectral methods to large, sparse networks is both the theoretical and practical centre of the research and development that has gone into MultiNet. Spectral methods provide analytic visualizations of network data: pictures that not only provide understanding, but that provide numerical values that can be used in further analysis. The results of the spectral methods, as well as other attribute and network data, are used together with simple, standard statistical methods such as cross-tabulations, analysis of variance and correlations for testing hypotheses about relationships among the data. MultiNet provides unique methods that allow attributes and networks to be freely mixed in such analyses, and presents results in both textual and interactive visualizations that include two or three discrete or continuous variables. The largest part of this thesis consists of descriptions of the seven main MultiNet program modules. Supplementary sections describe the theoretical background for spectral analysis and provide specific examples of spectral analysis, including a peer-reviewed, published paper that uses most of the parts of MultiNet together. In addition, a separate CDROM provides a working version ofthe program, electronic documentation, sample datasets, software aids and videos showing how the program is used

Negative eigenvectors, long paths and p*

Draft- not for citation or distribution We will discuss the roles of positive and negative eigenvalues of the Normal spectrum in identifying long paths in a network. These roles may be understood in terms of the "vibrational modes " of the associated eigenvectors. Nodes clustered together in an off-diagonal (almost bipartite) blockmodel may in fact be quite far apart in either graph-theoretic or random walk distance, especially in large sparse networks. We use p * as a tool to evaluate the blockmodels based on eigenvector partitions. We will also discuss fitting p * models large networks, recently added to MultiNet

Partitioning Networks by Eigenvectors

A survey of published methods for partitioning sparse arrays is presented. These include early attempts to describe the partitioning properties of eigenvectors of the adjacency matrix. More direct methods of partitioning are developed by introducing the Laplacian of the adjacency matrix via the directed (signed) edge-vertex incidence matrix. It is shown that the Laplacian solves the minimization of total length of connections between adjacent nodes, which induces clustering of connected nodes by partitioning the underlying graph. Another matrix derived from the adjacency matrix is also introduced via the unsigned edge-vertex matrix. This (the Normal) matrix is not symmetric, and it also is shown to solve the minimization of total length in its own non-Euclidean metric. In this case partitions are induced by clustering the connected nodes. The Normal matrix is closely related to Correspondence Analysis

Small and other worlds: Global network structures from local processes

this research, and for the helpful comments of two reviewers. This research was conducted with support from the Australian Research Council, and was supported in part by grants from the NIH (R01-DA012831 and R01-HD041877). Using a simulation approach based on the Metropolis algorithm, we contrast broad global features of network structure – in particular, small world properties – with the local patterning that could generate the network. It is not difficult to infer local structures emerging from certain simple social processes but, as these localized patterns agglomerate, the global outcomes are often not apparent. In such cases, computational techniques are necessary because analytic solutions are simply not available. In this paper, we show how to simulate a distribution of Markov random graphs based on assumptions about simple local social processes. We examine the resulting global structures by comparison with an appropriate Bernoulli distribution of graphs and provide examples of various stochastic global “worlds ” that may result, including small worlds, long path worlds and dense non-clustered worlds with many four-cycles. In the light of these results we suggest a locally-specified social process that may result in small-world global properties. In examining the movement from structure to randomness, we show how parameter scaling relates to a phase transition occurring at a certain scaling (“temperature”) so that a regular structure “melts ” into a stochasticallybased counterpart. We provide examples of “frozen ” deterministic structures, including highly clustered “caveman ” graphs, bipartite structures, and global cyclic structures involving structurally equivalent groups. 1

Networks of Symptoms and Exposures

We present some novel methods for analyzing and visualizing data from medical studies using methods originally developed for the study of social networks. The methods are based on spectral (eigendecomposition) properties of networks, in particular the so-called Normal spectrum. Among the many desirable properties of this spectrum is the natural handling of bipartite (2-mode) networks through negative eigenvalues, the clustering properties related to positive eigenvalues, and the relationship to the chi-squared measure of dependence in contingency tables

Revenue loss due to whale entanglement mitigation and fishery closures.

Whale entanglements with fishing gear, exacerbated by changing environmental conditions, pose significant risk to whale populations. Management tools used to reduce entanglement risk, for example temporary area restrictions on fishing, can have negative economic consequences for fishing communities. Balancing whale protection with sustaining productive fisheries is therefore a challenge experienced worldwide. In the California Current Ecosystem, ecosystem indicators have been used to understand the environmental dynamics that lead to increased whale entanglement risk in a lucrative crab fishery. However, an assessment of socio-economic risk for this fishery, as in many other regions, is missing. We estimate retrospectively the losses from ex-vessel revenue experienced by commercial Dungeness crab fishers in California during two seasons subject to whale entanglement mitigation measures using a Linear-Cragg hurdle modeling approach which incorporated estimates of pre-season crab abundance. In the 2020 fishing season, our results suggest total revenues would have been $14.4 million higher in the Central Management Area of California in the absence of closures and other disturbances. In the 2019 fishing season, our results suggest ex-vessel revenues would have been$9.4 million higher in the Central Management Area and $0.3 million higher in the Northern Management Area. Our evaluation should motivate the development of strategies which maximize whale protection whilst promoting productive, sustainable and economically-viable fisheries