We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Implementation science has progressed towards increased use of theoretical approaches to provide better understanding and explanation of how and why implementation succeeds or fails. The aim of this article is to propose a taxonomy that distinguishes between different categories of theories, models and frameworks in implementation science, to facilitate appropriate selection and application of relevant approaches in implementation research and practice and to foster cross-disciplinary dialogue among implementation researchers. Theoretical approaches used in implementation science have three overarching aims: describing and/or guiding the process of translating research into practice (process models); understanding and/or explaining what influences implementation outcomes (determinant frameworks, classic theories, implementation theories); and evaluating implementation (evaluation frameworks). This article proposes five categories of theoretical approaches to achieve three overarching aims. These categories are not always recognized as separate types of approaches in the literature. While there is overlap between some of the theories, models and frameworks, awareness of the differences is important to facilitate the selection of relevant approaches. Most determinant frameworks provide limited “how-to” support for carrying out implementation endeavours since the determinants usually are too generic to provide sufficient detail for guiding an implementation process. And while the relevance of addressing barriers and enablers to translating research into practice is mentioned in many process models, these models do not identify or systematically structure specific determinants associated with implementation success. Furthermore, process models recognize a temporal sequence of implementation endeavours, whereas determinant frameworks do not explicitly take a process perspective of implementation.

/pdf/making-sense-of-implementation-theories-models-and-9m1o7axeoi.pdf

Making sense of implementation theories, models and frameworks

https://www.linkgroup.hu/docs/13PharmTher.pdf

Structure and dynamics of molecular networks: A novel paradigm of drug discovery: A comprehensive review

Terrorist attacks on transportation networks have traumatized modern societies. With a single blast, it has become possible to paralyze airline traffic, electric power supply, ground transportation or Internet communication. How and at which cost can one restructure the network such that it will become more robust against a malicious attack? We introduce a new measure for robustness and use it to devise a method to mitigate economically and efficiently this risk. We demonstrate its efficiency on the European electricity system and on the Internet as well as on complex networks models. We show that with small changes in the network structure (low cost) the robustness of diverse networks can be improved dramatically whereas their functionality remains unchanged. Our results are useful not only for improving significantly with low cost the robustness of existing infrastructures but also for designing economically robust network systems.

/pdf/mitigation-of-malicious-attacks-on-networks-3vgg1gyljk.pdf

Mitigation of malicious attacks on networks

動注化学療法における pharmacokinetics と臨床

Intentional islanding of a power system can be an emergency response for isolating failures that might propagate and lead to major disturbances. Some of the islanding techniques suggested previously do not consider the power flow model; others are designed to minimize load shedding only within the islands. Often these techniques are computationally expensive. We aim to find approaches to partition power grids into islands to minimize the load shedding not only in the region where the failures start, but also in the topological complement of the region. We propose a new constraint programming formulation for optimal islanding in power grid networks. This technique works efficiently for small networks but becomes expensive as size increases. To address the scalability problem, we propose two grid partitioning methods based on modularity, properly modified to take into account the power flow model. They are modifications of the Fast Greedy algorithm and the Bloom algorithm, and are polynomial in running time. We tested these methods on the available IEEE test systems. The Bloom type method is faster than the Fast Greedy type, and can potentially provide results in networks with thousands of nodes. Our methods provide solutions which retain at least 40-50% of the system load. Overall, our methods efficiently balance load shedding and scalability.

/pdf/optimal-intentional-islanding-to-enhance-the-robustness-of-2zgv0mp83c.pdf

Optimal intentional islanding to enhance the robustness of power grid networks

Expressions and bounds for Newman’s modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the assortativity of the graph is changed via degree-preserving rewiring. Via simulations, we show that the maximum modularity increases, the number of clusters decreases, and the average hop count and the effective graph resistance increase with increasing assortativity.

https://www.nas.ewi.tudelft.nl/people/Piet/papers/PhysRevE2010_modularity_assortativity.pdf

Spectral graph analysis of modularity and assortativity.

With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper investigates the characteristics of network topologies that maintain a high level of throughput in spite of multiple attacks. To this end, we select network topologies belonging to the main network models and some real world networks. We consider three types of attacks: removal of random nodes, high degree nodes, and high betweenness nodes. We use elasticity as our robustness measure and, through our analysis, illustrate that different topologies can have different degrees of robustness. In particular, elasticity can fall as low as 0.8% of the upper bound based on the attack employed. This result substantiates the need for optimized network topology design. Furthermore, we implement a tradeoff function that combines elasticity under the three attack strategies and considers the cost of the network. Our extensive simulations show that, for a given network density, regular and semi-regular topologies can have higher degrees of robustness than heterogeneous topologies, and that link redundancy is a sufficient but not necessary condition for robustness.

/pdf/characterizing-the-robustness-of-complex-networks-knxxpclm45.pdf

Characterizing the Robustness of Complex Networks

The study of epidemics is a crucial issue to several areas. An epidemic can have devastating economic and social consequences. A single crop disease in Kansas could destroy the yearly income of many farmers. Previous work using graph theory has determined a universal epidemic threshold found in the graph topology for a binary contact network in the compartmental susceptible-infected (SI) analysis. We expand this threshold to a more realistic measure. A binary uniform level of contact within a society is too idealistic and an improved threshold is found in allowing a spectrum of contact within a contact network. The expanded contact network also allows for asymmetric contact such as a mother caring for her child. Further study in this area should lead to improved simulators, disease modeling, policies and control of infectious diseases and viruses.

Epidemic spreading on weighted contact networks

Just as a herd of animals relies on its robust social structure to survive in the wild, similarly robustness is a crucial characteristic for the survival of a complex network under attack. The capacity to measure robustness in complex networks defines a network's survivability in the advent of classical component failures and at the onset of cryptic malicious attacks. To date, robustness metrics are deficient and unfortunately the following dilemmas exist: accurate models necessitate complex analysis while conversely, simple models lack applicability to our definition of robustness. In this paper, we define robustness and present a novel metric, elasticity- a bridge between accuracy and complexity-a link in the chain of network robustness. Additionally, we "test-drive" the performance of elasticity on Internet topologies and online social networks, and articulate results.

/pdf/elasticity-topological-characterization-of-robustness-in-57yjvrkfty.pdf

Phillip Schumm

Papers

Optimal intentional islanding to enhance the robustness of power grid networks

Spectral graph analysis of modularity and assortativity.

Characterizing the Robustness of Complex Networks

Epidemic spreading on weighted contact networks

Elasticity: topological characterization of robustness in complex networks