Theoretical exploration of network structure significance requires a range of different networks for comparison. Here, we present a new method to construct networks in a spatial setting that uses spectral methods in combination with a probability distribution function. Nearly all previous algorithms for network construction have assumed randomized distribution of links or a distribution dependent on the degree of the nodes. We relax those assumptions. Our algorithm is capable of creating spectral networks along a gradient from random to highly clustered or diverse networks. Number of nodes and link density are specified from start and the structure is tuned by three parameters (gamma, sigma, kappa). The structure is measured by fragmentation, degree assortativity, clustering and group betweenness of the networks. The parameter gamma regulates the aggregation in the spatial node pattern and sigma and kappa regulates the probability of link forming.

Network measures are used to predict the behavior of different systems. To be able to investigate how various structures behave and interact we need a wide range of theoretical networks to explore. Both spatial and non-spatial methods exist for generating networks but they are limited in the ability of producing wide range of network structures. We extend an earlier version of a spatial spectral network algorithm to generate a large variety of networks across almost all the theoretical spectra of the following network measures: average clustering coefficient, degree assortativity, fragmentation index, and mean degree. We compare this extended spatial spectral network-generating algorithm with a non-spatial algorithm regarding their ability to create networks with different structures and network measures. The spatial spectral network-generating algorithm can generate networks over a much broader scale than the non-spatial and other known network algorithms. To exemplify the ability to regenerate real networks, we regenerate networks with structures similar to two real Swedish swine transport networks. Results show that the spatial algorithm is an appropriate model with correlation coefficients at 0.99. This novel algorithm can even create negative assortativity and managed to achieve assortativity values that spans over almost the entire theoretical range.

Missing links due to sampling difficulties can be a limitation in network analysis. Measurements and analysis of networks with insufficient data may make the actual properties indistinct and thus include too much uncertainty to lead to accurate inferences. In addition, in dynamical networks with low link degrees and high stochasticity one sample of the network structure during a finite time window may not be sufficient for general conclusions. Our interest here is to examine the possible consequences of analysis of networks with insufficient data. We studied how mean link degree in sampled networks affects predictions of the spread of disease. Networks with weighted links were used to run scenarios that assumed distance-dependent probabilities of disease transmission when applying general simulation methodology. These scenarios were compared with scenarios including randomly drawn probabilities of disease transmission. For both types of scenarios, we also tested two link-forming methods, one based on distance-dependence and the other on a random approach. Our findings imply that sampled networks must be improved by using statistical measures before attempting to estimate or predict the spread of disease. We conclude that, under the assumption of weighted links, predictions about the extent of an epidemic can be drawn only at mean degrees that are much higher than found in empirical studies. In reality, neither sampling procedures nor disease transmissions are completely dependent on distance. Our results show how this aspect enforces an even higher level of mean degree to be present in order to achieve reasonable predictions.

Networks can be categorised using different measures of connectivity and topology of the network. We have examined if such network measures can be used as predictors of disease transmission in networks. In this study, virtual networks with a wide range of different structures are generated using the SpecNet algorithm. Measures are calculated for both the network as a whole and for individual nodes. The virtual networks generated a large variation in number of infected farms. In general, a large variation was still present for networks with equal value of a measure which implies that single network measures may not be sufficient as predictor for spread of disease. Yet, mean degree and the average clustering coefficient were the global network measures that could best explain the variation in the number of infected farms of a network. At the local level the degree and the clustering coefficient of the initially infected farm explain most of the variation in the number of infected farms. Hence, our results also points out that one should also consider the characteristics of the initially infected farm when predicting  the spread of a disease.