Critical Nodes In Directed Networks

Critical nodes or "middlemen" have an essential place in both social and economic networks when considering the flow of information and trade. This paper extends the concept of critical nodes to directed networks. We identify strong and weak middlemen. Node contestability is introduced as a form of competition in networks; a duality between uncontested intermediaries and middlemen is established. The brokerage power of middlemen is formally expressed and a general algorithm is constructed to measure the brokerage power of each node from the networks adjacency matrix. Augmentations of the brokerage power measure are discussed to encapsulate relevant centrality measures. We use these concepts to identify and measure middlemen in two empirical socio-economic networks, the elite marriage network of Renaissance Florence and Krackhardt's advice network.Comment: 28 pages, 6 figures, 2 table

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting "accelerating" growth have total link numbers growing faster than linearly with network size and can exhibit transitions from stationary to nonstationary statistics and from random to scale-free to regular statistics at particular critical network sizes. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value.Comment: Corrected error in biological input parameter: 15 pages, 10 figure

Percolation in the Secrecy Graph

The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers, which, in the model, is determined solely by the locations of the nodes and eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the locations of the nodes and eavesdroppers are given by Poisson point processes, and present bounds for different types of percolation, including in-, out- and undirected percolation.Comment: 22 pages, 3 figure

Early fragmentation in the adaptive voter model on directed networks

We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process may be relevant for fragmentation in current political opinion formation processes.Comment: 9 pages, 8 figures as published in Phys. Rev.

Statistical Tools for Directed and Bipartite Networks

Directed networks and bipartite networks, which exhibit unique asymmetric connectivity structures, are commonly observed in a variety of scientific and engineering fields. Despite their abundance and utility, most network analysis methods only consider symmetric networks. In this thesis, we develop statistical methods and theory for directed and bipartite networks. The first chapter focuses on matched community detection in a bipartite network. The detection of matched communities, i.e. communities that consist of nodes of two types that are closely connected with one another, is a fundamental and challenging problem. Most widely used approaches for matched community detection are either computationally inefficient or prone to non-ideal performance. We propose a new two-stage algorithm that uses fast spectral methods to recover matched communities. We show that, for bipartite networks, it is critical to adjust for the community size in matched community detection, which had not been considered before. We also provide theoretical error bounds for the proposed algorithm on the number of mis-clustered nodes under a variant of the stochastic block model. Numerical studies indicate that the proposed method outperforms existing spectral algorithms, especially when the sizes of the matched communities are proportionally different between the two types. The second chapter of the thesis introduces a new preference-based block model for community detection in a directed network. Unlike existing models, the proposed model allows different sender nodes to have different preferences to communities in the network. We argue that the right singular vectors of a graph Laplacian matrix contain community structures under the model. Further, we propose a spectral clustering algorithm to detect communities and estimate parameters of the model. Theoretical results show insights on how the heterogeneity of preferences and out-degrees contribute to an upper bound of the number of mis-clustered nodes. Numerical studies support the theoretical results and illustrate the outstanding performance of the proposed method. The model can also be naturally extended to bipartite networks. In the third chapter, we propose a dyadic latent space model which accommodates the reciprocity between a pair of nodes in directed networks. Nodes in a pair in directed networks often exhibit strong dependencies with each other, though most widely used approaches usually account for this phenomenon with limited flexibility. We propose a new latent space model for directed networks that incorporates the reciprocity in a flexible way, allowing for important characteristics such as homophily and heterogeneity of the nodes. A fast and scalable algorithm based on projected gradient descent has been developed to fit the model by maximizing the likelihood. Both simulation studies and real-world data examples illustrate that the proposed model is effective in various network analysis tasks including link prediction and community detection.PHDStatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163156/1/yoohs_1.pd

An Energy Efficient, Load Balancing, and Reliable Routing Protocol for Wireless Sensor Networks

AN ENERGY EFFICIENT, LOAD BALANCING, AND RELIABLE ROUTING PROTOCOL FOR WIRELESS SENSOR NETWORKS by Kamil Samara The University of Wisconsin-Milwaukee, 2016 Under the Supervision of Professor Hossein Hosseini The Internet of Things (IoT) is shaping the future of Computer Networks and Computing in general, and it is gaining ground very rapidly. The whole idea has originated from the pervasive presence of a variety of things or objects equipped with the internet connectivity. These devices are becoming cheap and ubiquitous, at the same time more powerful and smaller with a variety of onboard sensors. All these factors with the availability of unique addressing, provided by the IPv6, has made these devices capable of collaborating with each other to accomplish common tasks. Mobile AdHoc Networks (MANETS) and Wireless Sensor Networks (WSN) in particular play a major role in the backbone of IoT. Routing in Wireless Sensor Networks (WSN) has been a challenging task for researchers in the last several years because the conventional routing algorithms, such as the ones used in IP-based networks, are not well suited for WSNs because these conventional routing algorithms heavily rely on large routing tables that need to be updated periodically. The size of a WSN could range from hundreds to tens of thousands of nodes, which will make routing tables’ size very large. Managing large routing tables is not feasible in WSNs due to the limitations of resources. The directed diffusion algorithm is a well-known routing algorithm for Wireless Sensor Networks (WSNs). The directed diffusion algorithm saves energy by sending data packets hop by hop and by enforcing paths to avoid flooding. The directed diffusion algorithm does not attempt to find the best or healthier paths (healthier paths are paths that use less total energy than others and avoid critical nodes). Hence the directed diffusion algorithm could be improved by enforcing the use of healthier paths, which will result in less power consumption. We propose an efficient routing protocol for WSNs that gives preference to the healthier paths based on the criteria of the total energy available on the path, the path length, and the avoidance of critical nodes. This preference is achieved by collecting information about the available paths and then using non-incremental machine learning to enforce path(s) that meet our criteria. In addition to preferring healthier paths, our protocol provides Quality of Service (QoS) features through the implementation of differentiated services, where packets are classified as critical, urgent, and normal, as defined later in this work. Based on this classification, different packets are assigned different priority and resources. This process results in higher reliability for the delivery of data, and shorter delivery delay for the urgent and critical packets. This research includes the implementation of our protocol using a Castalia Simulator. Our simulation compares the performance of our protocol with that of the directed diffusion algorithm. The comparison was made on the following aspects: • Energy consumption • Reliable delivery • Load balancing • Network lifetime • Quality of service Simulation results did not point out a significant difference in performance between the proposed protocol and the directed diffusion algorithm in smaller networks. However, when the network’s size started to increase the results showed better performance by the proposed protocol

Homogeneous and Scalable Gene Expression Regulatory Networks with Random Layouts of Switching Parameters

We consider a model of large regulatory gene expression networks where the thresholds activating the sigmoidal interactions between genes and the signs of these interactions are shuffled randomly. Such an approach allows for a qualitative understanding of network dynamics in a lack of empirical data concerning the large genomes of living organisms. Local dynamics of network nodes exhibits the multistationarity and oscillations and depends crucially upon the global topology of a "maximal" graph (comprising of all possible interactions between genes in the network). The long time behavior observed in the network defined on the homogeneous "maximal" graphs is featured by the fraction of positive interactions ($0\leq \eta\leq 1$) allowed between genes. There exists a critical value $\eta_c<1$ such that if $\eta<\eta_c$, the oscillations persist in the system, otherwise, when $\eta>\eta_c,$ it tends to a fixed point (which position in the phase space is determined by the initial conditions and the certain layout of switching parameters). In networks defined on the inhomogeneous directed graphs depleted in cycles, no oscillations arise in the system even if the negative interactions in between genes present therein in abundance ($\eta_c=0$). For such networks, the bidirectional edges (if occur) influence on the dynamics essentially. In particular, if a number of edges in the "maximal" graph is bidirectional, oscillations can arise and persist in the system at any low rate of negative interactions between genes ($\eta_c=1$). Local dynamics observed in the inhomogeneous scalable regulatory networks is less sensitive to the choice of initial conditions. The scale free networks demonstrate their high error tolerance.Comment: LaTeX, 30 pages, 20 picture

Percolation and reinforcement on complex networks

Complex networks appear in almost every aspect of our daily life and are widely studied in the fields of physics, mathematics, finance, biology and computer science. This work utilizes percolation theory in statistical physics to explore the percolation properties of complex networks and develops a reinforcement scheme on improving network resilience. This dissertation covers two major parts of my Ph.D. research on complex networks: i) probe—in the context of both traditional percolation and k-core percolation—the resilience of complex networks with tunable degree distributions or directed dependency links under random, localized or targeted attacks; ii) develop and propose a reinforcement scheme to eradicate catastrophic collapses that occur very often in interdependent networks. We first use generating function and probabilistic methods to obtain analytical solutions to percolation properties of interest, such as the giant component size and the critical occupation probability. We study uncorrelated random networks with Poisson, bi-Poisson, power-law, and Kronecker-delta degree distributions and construct those networks which are based on the configuration model. The computer simulation results show remarkable agreement with theoretical predictions. We discover an increase of network robustness as the degree distribution broadens and a decrease of network robustness as directed dependency links come into play under random attacks. We also find that targeted attacks exert the biggest damage to the structure of both single and interdependent networks in k-core percolation. To strengthen the resilience of interdependent networks, we develop and propose a reinforcement strategy and obtain the critical amount of reinforced nodes analytically for interdependent Erdős-Rényi networks and numerically for scale-free and for random regular networks. Our mechanism leads to improvement of network stability of the West U.S. power grid. This dissertation provides us with a deeper understanding of the effects of structural features on network stability and fresher insights into designing resilient interdependent infrastructure networks