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We investigate three related problems concerning sampling minorities in attributed networks. This is guided by a general attributed network model which can incorporate several levels of homophily and heterophily, and whose degree and Page-rank distributions have known properties. The first problem investigates sampling schemes that favor the representation of the minority over majority nodes and give preference to "more popular" minority nodes (i.e. higher degree/Page-rank) for a given homophily scenario. We show that (in-)degree and Page-rank sampling schemes increase the probability of sampling a minority node. The second problem concerns the relative ranking of minorities compared to majorities in degree and Page-rank based sampling schemes for several homophily and heterophily scenarios. We provide analytical conditions for the minority nodes to rank higher as a function of the model parameters for the degree based samplings and investigate the problem numerically for Page-rank based sampling schemes. The third problem considers subgraph sampling schemes and the bias of the proportion of minority nodes in top ranked degree nodes in several homophily and heterophily scenarios. Finally, the results and findings obtained from the sampling analysis are assessed on real-world networks. [ABSTRACT FROM AUTHOR]

Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers. [ABSTRACT FROM AUTHOR]

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, N. In this paper, we present a novel derivation of the small-world property for Gilbert–Erdös–Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime. [ABSTRACT FROM AUTHOR]

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment rules. When a new edge is created, with probability p ∈ (0 , 1) , it follows the PA rule. Otherwise, this new edge is added between two uniformly chosen nodes. Such mixture makes the in- and out-degrees of a fixed node grow at a slower rate, compared to the pure PA case, thus leading to lighter distributional tails. For estimation and inference, we develop two numerical methods which are applied to both synthetic and real network data. We see that with extra flexibility given by the parameter p, the hybrid random network provides a better fit to real-world scenarios, where lighter tails from in- and out-degrees are observed. [ABSTRACT FROM AUTHOR]

Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree distributions, number of edges, and other relevant network metrics which support the scale-free structure of networks. Previous work on such graphs imposes a marginal assumption of univariate regular variation (e.g., power-law tail) on the bivariate generating graphex function. In this paper, we study sparse exchangeable graphs generated by graphex functions which are multivariate regularly varying. We also focus on a different metric for our study: the distribution of the number of common vertices (connections) shared by a pair of vertices. The number being high for a fixed pair is an indicator of the original pair of vertices being connected. We find that the distribution of number of common connections are regularly varying as well, where the tail indices of regular variation are governed by the type of graphex function used. Our results are verified on simulated graphs by estimating the relevant tail index parameters. [ABSTRACT FROM AUTHOR]

Understanding charge transport mechanisms in thin-film transistors based on random networks of single-wall carbon nanotubes (SWCNT-TFTs) is essential for further advances to improve the potential for various nanoelectronic applications. Herein, a comprehensive investigation of the two-dimensional (2D) charge transport mechanism in SWCNT-TFTs is reported by analyzing the temperature-dependent electrical characteristics determined from the direct-current and non-quasi-static transient measurements at 80–300 K. To elucidate the time-domain charge transport characteristics of the random networks in the SWCNTs, an empirical equation was derived from a theoretical trapping model, and a carrier velocity distribution was determined from the differentiation of the transient response. Furthermore, charge trapping and de-trapping in shallow- and deep-traps in SWCNT-TFTs were analyzed by investigating charge transport based on their trapping/de-trapping rate. The comprehensive analysis of this study provides fundamental insights into the 2D charge transport mechanism in TFTs based on random networks of nanomaterial channels. [ABSTRACT FROM AUTHOR]

Epilepsy has been found to be modulated by the astrocyte systems in experiments, and tremendous modeling studies have unveiled the roles of astrocyte cellular functions such as the calcium and potassium channels in the epileptic seizures. However, little attention has been paid to the structure changes of astrocytes in the epileptic seizures in the scale of networks. This paper first constructs a neuron–astrocyte network model to explain the experimental observation that astrocytes mainly induce epilepsy by blocking the channels of the astrocyte gap junction in the network scale. Such model is used to discuss potential seizure induction process in the network by changing the connection intensity of the astrocyte gap junction. The simulation results show that a decrease of the gap junction intensity changes the firing pattern of the population of neurons from slow periodical firing to high-frequency epileptic seizures, featuring epileptic patterns of depolarization blocks. This further verifies that epileptic seizures are experimentally induced via the channel block of the astrocyte gap junctions. Because of the heterogeneous structure of the real neuron–astrocyte network, the effect of changing astrocyte network structures on the seizure activities is then studied in two typical network structures: the regular neighboring connection and the random connection. The results show that an increase of the number of regular connections of the regular neighboring astrocyte network could inhibit the induction and spread of the epileptic seizures. The epileptic inhibition can be achieved similarly by increasing the connection probability of the random astrocyte network. These findings further provide evidence for the experimental phenomena of the protective response of gliosis to epilepsy with increasing gap junctions. Above all, the simulation results suggest a potential pathway of epilepsy treatment by targeting the astrocyte gap junctions. [ABSTRACT FROM AUTHOR]

Cellulose nanopapers provide diverse, strong and lightweight templates prepared entirely from sustainable raw materials, cellulose nanofibers (CNFs). Yet the strength of CNFs has not been fully capitalized in the resulting nanopapers and the relative influence of CNF strength, their bonding, and biological origin to nanopaper strength are unknown. Here, we show that basic principles from paper physics can be applied to CNF nanopapers to illuminate those relationships. Importantly, it appeared that ~ 200 MPa was the theoretical maximum for nanopapers with random fibril orientation. Furthermore, we demonstrate the contrast in tensile strength for nanopapers prepared from bacterial cellulose (BC) and wood-based nanofibrillated cellulose (NFC). Endemic amorphous polysaccharides (hemicelluloses) in NFC act as matrix in NFC nanopapers, strengthening the bonding between CNFs just like it improves the bonding between CNFs in the primary cell wall of plants. The conclusions apply to all composites containing non-woven fiber mats as reinforcement. [ABSTRACT FROM AUTHOR]

A novel parallel algorithm is presented for generating random scale-free networks using the preferential attachment model. The algorithm, named cuPPA, is custom-designed for "single instruction multiple data (SIMD)" style of parallel processing supported by modern processors such as graphical processing units (GPUs). To the best of our knowledge, our algorithm is the first to exploit GPUs, and also the fastest implementation available today, to generate scale-free networks using the preferential attachment model. A detailed performance study is presented to understand the scalability and runtime characteristics of the cuPPA algorithm. Also another version of the algorithm called cuPPA-Hash tailored for multiple GPUs is presented. On a single GPU, the original cuPPA algorithm delivers the best performance, but is challenging to port to multi-GPU implementation. For multi-GPU implementation, cuPPA-Hash has been used as the parallel algorithm to achieve a perfect linear speedup up to 4 GPUs. In one of the best cases, when executed on an NVidia GeForce 1080 GPU, the original cuPPA generates a scale-free network of two billion edges in less than 3 s. On multi-GPU platforms, cuPPA-Hash generates a scale-free network of 16 billion edges in less than 7 s using a machine consisting of 4 NVidia Tesla P100 GPUs. [ABSTRACT FROM AUTHOR]

We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration flows and neuroscience. Analogous to fundamental results derived for standard (unweighted) exponential random graph models in the work of Chatterjee and Diaconis, we derive limiting results for the structure of these models as the number of nodes goes to infinity. Our results are applicable for a wide variety of base measures including measures with unbounded support. We also derive sufficient conditions for continuity of functionals in the specification of the model including conditions on nodal covariates. Finally we include a number of open problems to spur further understanding of this model especially in the context of applications. [ABSTRACT FROM AUTHOR]

In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent τ∈(2,3). We assign independent and identically distributed (i.i.d.) weights to the edges of the graph. We investigate the weighted distance (the length of the shortest weighted path) between two uniformly chosen vertices, called typical distances. When the underlying age-dependent branching process approximating the local neighborhoods of vertices is found to produce infinitely many individuals in finite time—called explosive branching process—Baroni, Hofstad and the second author showed in Baroni et al. (J Appl Probab 54(1):146-164, 2017) that typical distances converge in distribution to a bounded random variable. The order of magnitude of typical distances remained open for the τ∈(2,3) case when the underlying branching process is not explosive. We close this gap by determining the first order of magnitude of typical distances in this regime for arbitrary, not necessary continuous edge-weight distributions that produce a non-explosive age-dependent branching process with infinite mean power-law offspring distributions. This sequence tends to infinity with the amount of vertices, and, by choosing an appropriate weight distribution, can be tuned to be any growing function that is O(loglogn), where n is the number of vertices in the graph. We show that the result remains valid for the the erased configuration model as well, where we delete loops and any second and further edges between two vertices. [ABSTRACT FROM AUTHOR]

This paper concerns the SIR dynamics with two types of spreading mechanism, i.e., local spreading through network contacts and global spreading through casual contacts. A low-dimensional edge-based model of ordinary differential equations incorporating arbitrary heterogeneous number of individual contacts is formulated. The basic reproduction number $$R_{0}$$ is obtained, and on networks of Poisson type, it is the sum of the basic reproduction numbers for global and local spreading pathways; however, on networks of other type, it is a nonlinear function of the basic reproduction numbers for global and local spreading pathways. To measure the control efforts imposed on one specific transmission pathway, type reproduction numbers for global and local transmission pathways are calculated, respectively. Equations of the final epidemic size are analytically derived. Finally, the numerical solutions to our model are compared with the ensemble averages of the stochastic simulations. Simulations have shown that casual contacts in the population may trigger large stochastic fluctuations, which may cause huge variances around their mean; thus, in this scenario the ensemble mean is not a good representation of the behavior of the stochastic epidemic process. However, increasing the local infection rate or the connectedness of networks yields better predictions. The results presented provide insights in setting a framework for the analysis and containment of multiple routes of epidemic transmission in reality. [ABSTRACT FROM AUTHOR]

In this paper we study typical distances in the configuration model, when the degrees have asymptotically infinite variance. We assume that the empirical degree distribution follows a power law with exponent $$\tau \in (2,3)$$ , up to value $$n^{{\beta _n}}$$ for some $${\beta _n}\gg (\log n)^{-\gamma }$$ and $$\gamma \in (0,1)$$ . This assumption is satisfied for power law i.i.d. degrees, and also includes truncated power-law empirical degree distributions where the (possibly exponential) truncation happens at $$n^{{\beta _n}}$$ . These examples are commonly observed in many real-life networks. We show that the graph distance between two uniformly chosen vertices centers around $$2 \log \log (n^{{\beta _n}}) / |\log (\tau -2)| + 1/({\beta _n}(3-\tau ))$$ , with tight fluctuations. Thus, the graph is an ultrasmall world whenever $$1/{\beta _n}=o(\log \log n)$$ . We determine the distribution of the fluctuations around this value, in particular we prove these form a sequence of tight random variables with distributions that show $$\log \log $$ -periodicity, and as a result it is non-converging. We describe the topology and number of shortest paths: We show that the number of shortest paths is of order $$n^{f_n{\beta _n}}$$ , where $$f_n \in (0,1)$$ is a random variable that oscillates with n. We decompose shortest paths into three segments, two 'end-segments' starting at each of the two uniformly chosen vertices, and a middle segment. The two end-segments of any shortest path have length $$\log \log (n^{{\beta _n}}) / |\log (\tau -2)|$$ +tight, and the total degree is increasing towards the middle of the path on these segments. The connecting middle segment has length $$1/({\beta _n}(3-\tau ))$$ +tight, and it contains only vertices with degree at least of order $$n^{(1-f_n){\beta _n}}$$ , thus all the degrees on this segment are comparable to the maximal degree. Our theorems also apply when instead of truncating the degrees, we start with a configuration model and we remove every vertex with degree at least $$n^{{\beta _n}}$$ , and the edges attached to these vertices. This sheds light on the attack vulnerability of the configuration model with infinite variance degrees. [ABSTRACT FROM AUTHOR]

With recent advances in networking technology, emerging networks continue to play an increasing role in the lives of most users. The Internet search and retrieval system is so powerful that it helps us to share information and perspectives from across the world. However, the threat of censorship exists on some centralized search engines, since all of their information is currently controlled by these sites administrators. The restriction and control of information are pervasive enough within governments and organizations to censor or intrude on even the most free and uncontrolled communication media. For this reason, the Peer-to-Peer (P2P) search and retrieval system is designed to resist censorship over the network. Nevertheless, its decentralized nature makes it very difficult to infer information that cannot be measured directly, such as the proportion of subverted and selfish nodes. Moreover, the situation is even more challenging when the network becomes extremely large. Hence, I propose a dynamic adaptive algorithm that can: 1) tackle the censorship and security issues; 2) determine the proportion of subverted and selfish nodes; 3) defend against malicious and selective forwarding attacks by appropriately adjusting the number of requests to ensure high match probability; 4) guarantee robustness and scalability even with different random networks and varied network sizes. In several experiments, I demonstrate that my algorithm can effectively and accurately estimate these metrics and manage the system, even when the network has a large proportion of malicious nodes, a large proportion of selfish nodes, or a mere partial view of network membership. [ABSTRACT FROM AUTHOR]

We study the problems of pricing an indivisible product to consumers who are embedded in a given social network. The goal is to maximize the revenue of the seller by the so-called iterative pricing that offers consumers a sequence of prices over time. The consumers are assumed to be impatient in that they buy the product as soon as the seller posts a price not greater than their valuations of the product. The product's value for a consumer is determined by two factors: a fixed consumer-specified intrinsic value and a variable externality that is exerted from the consumer's neighbors in a linear way. We focus on the scenario of negative externalities, which captures many interesting situations, but is much less understood in comparison with its positive externality counterpart. Assuming complete information about the network, consumers' intrinsic values, and the negative externalities, we prove that it is NP-hard to find an optimal iterative pricing, even for unweighted tree networks with uniform intrinsic values. Complementary to the hardness result, we design a 2-approximation algorithm for general weighted networks with (possibly) nonuniform intrinsic values. We show that, as an approximation to optimal iterative pricing, single pricing works fairly well for many interesting cases, such as forests, Erdős-Rényi networks and Barabási-Albert networks, although its worst-case performance can be arbitrarily bad in general networks. [ABSTRACT FROM AUTHOR]

We define the problem of maximal assortativity matching (MAM) as a variant of the maximal matching problem wherein we want to maximize the similarity between the end vertices (with respect to any particular measure for node weight) constituting the matching. The MAM algorithm (with a targeted assortative index value of 1) works on the basis of the assortative weight of an edge, defined as the product of the number of uncovered adjacent edges and the absolute difference of the weights of the end vertices of the edge. The MAM algorithm prefers to include the edge with the smallest assortativity weight (the assortative weight of the edges is updated for each iteration) until all the edges in the graph are covered. We show that the MAM algorithm can be easily adapted to be used for maximal dissortative matching (MDM) with a targeted assortative index of $$-$$ 1 for the matching as well as for maximal node matching (MNM) algorithm to maximize the percentage of nodes matched. We illustrate the execution of the MAM, MDM and MNM algorithms on complex network graphs such as the random network graphs and scale-free network graphs as well as on real-world network graphs and analyze the tradeoffs. [ABSTRACT FROM AUTHOR]

The Newman-Watts model is given by taking a cycle graph of n vertices and then adding each possible edge $$(i,j), |i-j|\ne 1 \mod n$$ with probability $$\rho /n$$ for some $$\rho >0$$ constant. In this paper we add i.i.d. exponential edge weights to this graph, and investigate typical distances in the corresponding random metric space given by the least weight paths between vertices. We show that typical distances grow as $$\frac{1}{\lambda }\log n$$ for a $$\lambda >0$$ and determine the distribution of smaller order terms in terms of limits of branching process random variables. We prove that the number of edges along the shortest weight path follows a Central Limit Theorem, and show that in a corresponding epidemic spread model the fraction of infected vertices follows a deterministic curve with a random shift. [ABSTRACT FROM AUTHOR]

We use mean field techniques to compute the distribution of excitatory and inhibitory firing rates in large networks of randomly connected spiking quadratic integrate and fire neurons. These techniques are based on the assumption that activity is asynchronous and Poisson. For most parameter settings these assumptions are strongly violated; nevertheless, so long as the networks are not too synchronous, we find good agreement between mean field prediction and network simulations. Thus, much of the intuition developed for randomly connected networks in the asynchronous regime applies to mildly synchronous networks. [ABSTRACT FROM AUTHOR]

We study the asymptotic throughput for a large-scale wireless ad hoc network consisting of n nodes under the generalized physical model. We directly compute the throughput of multicast sessions to unify the unicast and broadcast throughputs. We design two multicast schemes based on the so-called ordinary arterial road system and parallel arterial road system, respectively. Correspondingly, we derive the achievable multicast throughput by taking account of all possible cases of n = ω(1) and 1 ≤ n ≤ n − 1, rather than only the cases of $$n_s=\Uptheta(n)$$ as in most related works, where n and n denote the number of sessions and the number of destinations of each session, respectively. Furthermore, we consider the network with a general node density $$\lambda \in [1,n]$$, while the models in most related works are either random dense network (RDN) or random extended network (REN) where the density is λ = n and λ = 1, respectively, which further enhances the generality of this work. Particularly, for the special case of our results by letting λ = 1 and $$n_s=\Uptheta(n)$$, we show that for some regimes of n, the multicast throughputs achieved by our schemes are better than those derived by the well-known percolation-based schemes. [ABSTRACT FROM AUTHOR]

The discovery of small world properties in real-world networks has revolutionized the way we analyze and study real-world systems. Mathematicians and physicists in particular have closely studied and developed several models to artificially generate networks with small world properties. The classical algorithms to produce these graphs artificially make use of the fact that with the introduction of some randomness in ordered graphs, small world graphs can be produced. In this paper, we present a novel algorithm to generate graphs with small world properties based on the idea that with the introduction of some order in a random graph, small world graphs can be generated. Our model starts with a randomly generated graph. We then replace each node of the random graph with cliques of different sizes. This ensures that the connectivity between the cliques is random but the clustering coefficient increases to a desired level. We further extend this model to incorporate the property of community structures (clusters) found readily in real-world networks such as social, biological and technological networks. These community structures are densely connected regions of nodes in a network that are loosely connected to each other. The model generates these clustered small world graphs by replacing nodes in the random graph with densely connected set of nodes. Experimentation shows that these two models generate small world and clustered small world graphs, respectively, as we were able to produce the desired properties of a small world network with high clustering coefficient and low average path lengths in both cases. Furthermore, we also calculated relative density and modularity to show that the clustered networks indeed had community structures. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of disaster spreading in community networks. Unlike the case in other kinds of complex networks, the transitions between the self-healing and spreading dynamics for community networks are in ladder-type in dependent of the recovery time and time delay. Statistical analysis on the average erupting time of disaster in communities shows that large-scale disaster firstly erupts in the community with maximal average degree, which is unrelated with the location where the initial disturbance seed is. Moreover, the average erupting time of disaster reduces along with the decrease of the average degrees of communities. Therefore, the community structure is helpful on the control of the disaster spreading. [ABSTRACT FROM AUTHOR]

Self-sustained oscillations in complex networks consisting of nonoscillatory nodes have attracted long-standing interest in diverse natural and social systems. We study the self-sustained periodic oscillations in random networks consisting of excitable nodes. We reveal the underlying dynamic structure by applying a dominant phase-advanced driving method. The oscillation sources and wave propagation paths can be illustrated clearly via the dynamic structure revealed. Then we are able to control the oscillations with surprisingly high efficiency based on our understanding. [ABSTRACT FROM AUTHOR]

Data collection is one of the most important functions provided by wireless sensor networks. In this paper, we study theoretical limitations of data collection and data aggregation in terms of delay and capacity for a wireless sensor network where n sensors are randomly deployed. We consider different communication scenarios such as with single sink or multiple sinks, regularly-deployed or randomly-deployed sinks, with or without aggregation. For each scenario, we not only propose a data collection/aggregation method and analyze its performance in terms of delay and capacity, but also theoretically prove whether our method can achieve the optimal order (i.e., its performance is within a constant factor of the optimal). Particularly, with a single sink, the capacity of data collection is in order of $$\Uptheta(W)$$ where W is the fixed data-rate on individual links. With k regularly deployed sinks, the capacity of data collection is increased to $$\Uptheta(kW)$$ when $$k=O\left({\frac{n}{\log n}}\right)$$ or $$\Uptheta\left({\frac{n}{\log n}}W\right)$$ when $$k=\Upomega\left({\frac{n}{\log n}}\right)$$. With k randomly deployed sinks, the capacity of data collection is between $$\Uptheta\left({\frac{k}{\log k}}W\right)$$ and $$\Uptheta(kW)$$ when $$k=O\left({\frac{n}{\log n}}\right)$$ or $$\Uptheta\left({\frac{n}{\log n}}W\right)$$ when $$k=\omega\left({\frac{n}{\log n}}\right)$$. If each sensor can aggregate its receiving packets into a single packet to send, the capacity of data collection with a single sink is also increased to $$\Uptheta\left({\frac{n}{\log n}}W\right)$$. [ABSTRACT FROM AUTHOR]

We consider a random network evolving in continuous time in which new nodes are born and old may die, and where undirected edges between nodes are created randomly and may also disappear. The node population is Markovian and so is the creation and deletion of edges, given the node population. Each node is equipped with a random social index and the intensity at which a node creates new edges is proportional to the social index, and the neighbour is either chosen uniformly or proportional to its social index in a modification of the model. We derive properties of the network as time and the node population tends to infinity. In particular, the degree-distribution is shown to be a mixed Poisson distribution which may exhibit a heavy tail (e.g. power-law) if the social index distribution has a heavy tail. The limiting results are verified by means of simulations, and the model is fitted to a network of sexual contacts. [ABSTRACT FROM AUTHOR]

The study of network topologies provides interesting insights into the way in which the principles on which interconnected systems are constructed influence the dynamics of diffusion and communication processes in many kinds of socio-technical systems. Empirical research has shown that there are principles of construction similar to those of the laws of nature for social networks and their technical derivatives, like E-mail networks, the internet, publication co-authoring, or business collaboration. For decades, the paradigm of a randomly connected network has been used as a model for real world networks, in ignorance of the fact that they are only a poor fit for such networks. Apparently, all the above-mentioned networks share the same building blocks. They attach new members over time and the attachment prefers existing members that are already well connected. This principle of “preferential attachment” leads to interesting properties that have to be taken into consideration when analyzing and designing systems with some kind of network background. What are called “scale-free” networks seems to be a better fit for the description of real world networks. They use preferential attachment as a construction principle to resample real world networks. Their behavior in terms of diffusion and communication processes is fundamentally different from that of random networks. To illustrate the potential value of the discovery of scale-free networks for applications in information systems related research, an example will be used in this article to illustrate their usefulness for realistic network modeling. A scale-free communication network of security traders will show what impact network topology has on the dynamics of complex socio-technical systems. [ABSTRACT FROM AUTHOR]

The paper extends the Brock-Durlauf social interactions model to richer social structures modelled with arbitrary interaction topologies and examines in detail the star, the wheel and the path. It explores Nash equilibria when agents act on the basis of expectations over, and, alternatively, actual knowledge their neighbors’ decisions. It links social interactions with econometrics of systems of simultaneous equations. The local dynamics near steady states combine spectral properties of the adjacency matrix and of the nonlinearities of reaction functions. For regular interaction topologies, adjustment exhibit relative persistence. Cyclical interaction is associated with endogenous spatial oscillations and islands of conformity. [ABSTRACT FROM AUTHOR]

Using a natural metric on the space of networks, we define a probability measure for network-valued random variables. This measure is indexed by two parameters, which are interpretable as a location parameter and a dispersion parameter. From this structure, one can develop maximum likelihood estimates, hypothesis tests and confidence regions, all in the context of independent and identically distributed networks. The value of this perspective is illustrated through application to portions of the friedship cognitive social structure data gathered by Krackhardt (1987). [ABSTRACT FROM AUTHOR]