Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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We introduce an entropic prior for multinomial parameter estimation problems and solve for its maximum...

A central idea in marketing and diffusion research is that influentials—a minority of individuals who influence an exceptional number of their peers—are important to the formation of public opinion. Here we examine this idea, which we call the “influentials hypothesis,” using a series of computer simulations of interpersonal influence processes. Under most conditions that we consider, we find that large cascades of influence are driven not by influentials, but by a critical mass of easily influenced individuals. Although our results do not exclude the possibility that influentials can be important, they suggest that the influentials hypothesis requires more careful specification and testing than it has received.

In recent years, researchers have investigated a growing number of weighted networks where ties are differentiated according to their strength or capacity. Yet, most network measures do not take weights into consideration, and thus do not fully capture the richness of the information contained in the data. In this paper, we focus on a measure originally defined for unweighted networks: the global clustering coefficient. We propose a generalization of this coefficient that retains the information encoded in the weights of ties. We then undertake a comparative assessment by applying the standard and generalized coefficients to a number of network datasets. Key words: clustering, transitivity, weighted networks We wish to give very special thanks to Filip Agneessens, Stephen Borgatti, Carter Butts, and Tom Snijders for their valuable feedback on earlier versions of this paper. We are also grateful to participants of the 3 rd Conference on Applications of Social Network

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The small-world phenomenon, that the world’s social network is tightly connected, and that any two people can be linked by a short chain of friends, has long been a subject of interest. Famously, the psychologist Stanley Milgram performed an experiment where he asked people to deliver a letter to a stranger by forwarding it to an acquaintance, who could forward it to one his acquaintances, and so on until the destination was reached. The results seemed to confirm that the small-world phenomenon is real. Recently it has been shown by Jon Kleinberg that in order to search in a network, that is to actually find the short paths in the manner of the Milgram experiment, a very special type of a graph model is needed. In this thesis, we present two ideas about searching in the small world stemming from Kleinberg’s results. In the first we study the formation of networks of this type, attempting to see why the kind

How we act, as well as how we are acted upon, are to a large extent influenced by our relatives, friends and acquaintances. This is true of which profession we decide to pursue, whether or not we adopt a new technology, as well as whether or not we catch the flu. In this chapter we provide an overview of research that examines how social structure impacts

This paper experimentally investigates the service availability of wireless multihop networks based on the following two metrics: average pairwise connectivity and pairwise connected ratio, where the former denotes the average number of node-disjoint paths per node pair in a network and the latter is the fraction of node pairs that are pairwise connected. Further, a theoretical upper-bound has been derived for the average pairwise connectivity, which can approximate the exact value very well. Since in wireless multihop networks nodes may fail either naturally or maliciously, the fault tolerance and attack resilience are important issues. In this paper we have also studied the fault tolerance and attack resilience of wireless multihop networks, and proposed a new resilience metric, α-p-resilience, where a network is α-p-resilient if at least α portion of nodes pairs remain connected as long as no more than p fraction of nodes are removed from the network. Three different node removal patterns have been studied: random removal, selective removal according to node degree, and partition, and the experimental studies show that wireless multihop networks are more sensitive to partition attacks than random removal and selective removal attacks, and selective removal attacks are a little bit more severe than random removal attacks.

Abstract—In this paper we introduce the notion of protein interaction network. This is a graph whose vertices are the protein’s amino acids and whose edges are the interactions between them. Using a graph theory approach, we identify a number of properties of these networks. We compare them to the general small-world network model and we analyze their hierarchical structure. Keywords—interaction network, protein structure, small-world network. I.