Closeness Centralities of Lollipop Graphs

Closeness is one of the most studied characteristics of networks. Residual closeness is a very sensitive measure of graphs robustness. Additional closeness is a measure of growth potentials of networks. In this article we calculate the closeness, vertex residual closeness, link residual closeness, and additional closeness of lollipop graphs

Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.Comment: 21 pages, 13 figure

Mechanism of organization increase in complex systems

This paper proposes a variational approach to describe the evolution of organization of complex systems from first principles, as increased efficiency of physical action. Most simply stated, physical action is the product of the energy and time necessary for motion. When complex systems are modeled as flow networks, this efficiency is defined as a decrease of action for one element to cross between two nodes, or endpoints of motion - a principle of least unit action. We find a connection with another principle that of most total action, or a tendency for increase of the total action of a system. This increase provides more energy and time for minimization of the constraints to motion in order to decrease unit action, and therefore to increase organization. Also, with the decrease of unit action in a system, its capacity for total amount of action increases. We present a model of positive feedback between action efficiency and the total amount of action in a complex system, based on a system of ordinary differential equations, which leads to an exponential growth with time of each and a power law relation between the two. We present an agreement of our model with data for core processing units of computers. This approach can help to describe, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self-organization and robustness.Comment: 22 pages, 4 figures, 1 tabl

Centrality in networks of geographically proximate firms and competitive capabilities

We examine how a firm's centrality within a network of geographically proximate firms affects its competitive capabilities. Our study of the total population of one Spanish cluster of fishing firms shows that the effects of centrality on a firm's competitive capabilities are contingent on the effects of two relational characteristics of its direct ties: strength and degree of cognitive cohesion. Specifically, our results indicate that the centrality of a firm within the cluster network enhances its competitive capabilities as the strength of its direct ties increases. Further, firms can capture the value of centrality for enhancing competitive capabilities with a combination of strong (or weak) direct ties and low (or high) in degree of cognitive cohesion. We contribute to the network and strategy literatures by reconciling conflicting results with regard to the strategic benefits of a firm's centrality in a cluster and the relational characteristics of its direct ties

Structure-oriented prediction in complex networks

Complex systems are extremely hard to predict due to its highly nonlinear interactions and rich emergent properties. Thanks to the rapid development of network science, our understanding of the structure of real complex systems and the dynamics on them has been remarkably deepened, which meanwhile largely stimulates the growth of effective prediction approaches on these systems. In this article, we aim to review different network-related prediction problems, summarize and classify relevant prediction methods, analyze their advantages and disadvantages, and point out the forefront as well as critical challenges of the field

Link Residual Closeness of Harary Graphs

The study of networks characteristics is an important subject in differentfields, like math, chemistry, transportation, social network analysis etc. Theresidual closeness is one of the most sensitive measure of graphsvulnerability. In this article we calculate the link residual closeness ofHarary graphs.Comment: 15 page

Optimization of the transportation expense of a firm with contractual supplies

We consider nonlinear nonconvex capacitated transportation problems where the nonlinearity occurs only in the last row of the transportation tableau. This transportation model can be successfully applied to economics representing the nonlinearity caused by penalties for unsatisfied contractual quantities or by changing in price. An algorithm for local optimization, based on the algorithms for solving linear transportation problems, is suggested. It consists of three phases - initial, linear and nonlinear. The nonlinear phase uses auxiliary linear transportation problems. The algorithm is illustrated by proper examples. Sufficient conditions for satisfying contractual supplies are given.