Preferential attachment with choice-based edge step

Preferential attachment, also referred to as the “rich-get-richer” mechanism, characterizes the ability of already existing nodes in an evolutionary network to acquire new connections from newly-coming nodes throughout the growing process of the network. This mechanism is responsible for the emergence of some critical structures in many real networks, such as the Saccharomyces cerevisiae protein-protein interaction network, scientific collaboration network, and bitcoin transaction network. Clearly, it is very important to accurately estimate the preferential attachment mechanism for a growing network in interest. Although it has long been aware that the existing widely-used methods yield significantly biased estimates of preferential attachments, the underlying mechanism is not completely understood and not well explained. By rewriting preferential attachment from a deterministic formulation to a stochastic one, this paper reveals two major problems existing in the current methodologies, thereby well explaining why traditional methods introduce biases to the estimates of preferential attachments. To avoid the negative effects of these two problems, a new method is proposed based on the Poisson Pseudo Maximum Likelihood method for estimating preferential attachments, which provides asymptotically consistent estimation to preferential attachments. More importantly, even with insufficient information, the new method can still provide an estimate with high precision, showing a significant advantage in measuring preferential attachments based on small-sized samples. The new method is also robust against network parameter changes. The findings may shed some lights onto deeper understanding of the evolutionary processes of real networks.

We extend "stable marriage problem" studied via computer simulation (agent-based) from network perspective by dynamical generalization. We investigate how preferential or random attachment of individuals can affect simulation results such as: proportion of singles in society, number of divorces etc. We took into account attractiveness of individuals and its different types as well as personal taste. Current value of socio-economic pressure p (main model parameter) drives the dynamic of first marriage, remarriage or spontaneously marriage breaks up. Model reflects the behavior of the simplified heterosexual population (frequency of changing partners, the ratio of singles in society). Theoretical agent-based simulation (with populational approaches, e.g. Births and deaths) should be later supplemented by historical values of divorces/marriages in different countries of the world. Stable (constant) society was also implemented to show difference with "living" society. In this model, agents have attribute of attraction. Preferential attachment, known from network theory, was introduced, to mimic selection process. Additionally, totally random attachment (not attraction-depended) was also implemented for contrast.

A random k-out mapping (digraph) on [n] is generated by choosing k random images of each vertex one at a time, subject to a 'preferential attachment' rule: the current vertex selects an image i with probability proportional to a given parameter α = α(n) plus the number of times i has already been selected. Intuitively, the larger α becomes, the closer the resulting k-out mapping is to the uniformly random k-out mapping. We prove that α = Θ(n 1/2) is the threshold for α growing 'fast enough' to make the random digraph approach the uniformly random digraph in terms of the total variation distance. We also determine an exact limit for this distance for the α = β n 1/2 case.

In networked multiagent systems (NMASs) with resource caching, resource replicas are cached in favor of the agents who accessed such resources most recently and frequently. Task execution in NMASs is described through agents' operations when accessing necessary resources distributed in the networks, and thus, agents with richer experiences executing tasks will have higher access to resources. To optimize tasks' resource access time, we investigate two types of preferential attachments in the task allocation of NMASs with resource caching: history and present preferential attachments, in which an agent has higher access to a resource if that agent has richer history (or present) accessing experiences for that resource. Therefore, agents that were (or are) heavily burdened by tasks may have certain preferential rights to new tasks in the future. Our experiments found that preferential attachment in task allocation can effectively reduce tasks' execution time, particularly when the network context is considered and the number of tasks is high. In addition, we discovered two interesting phenomena: (1) Compromise between preferential attachment and load balancing can achieve better performance than single preferential attachment when there are too many tasks waiting, and (2) the integration of history and present preferential attachments can outperform either history or present preferential attachment alone in task allocation.

We study preferential attachment (i.e., a rich‐get‐richer effect) in alliance networks. Thereby, we argue that various levels (firm, firm group, country) influence the strength of preferential attachment. To test our hypotheses, we take a sample of 117 airlines from 74 countries in the period 2001 to 2011. For the estimation, we use stochastic actor‐oriented models, a method for analyzing longitudinal network data. As a result, we find that preferential attachment is stronger for firms that have fewer resources and are located in a less‐developed country. Consequently, we show how different competitive positions affect alliance strategies.

We analyze whether proximity effect, preferential attachment and path dependence or three "P" mechanisms would concur within the evolutionary process of inter-regional network. Using a unique database of China's technology transaction between regions, we show that proximity effect, preferential attachment and path dependence have coexisted in the evolutionary process of China's inter-regional network of technology transactions. In particular, the inter-regional relations positively and significantly correlate with the geographical and economic proximity matrix, all regions' three centrality values in current year positively and significantly correlate with their centrality in the last two years, and the inter-regional relations in current year positively and significantly correlate with own relations in last two years. This paper contributes to the existing literature by identifying three evolutionary mechanisms of inter-regional network. An interpretation is that the evolution process of inter-regional network is a very complex process, and one mechanism such as geographical proximity from the perspective of economic geography or preferential attachment from the perspective of network science only could explain a part of the process.

This paper proposes channels through which technological decoupling can affect global growth, and embeds these different layers in a global dynamic macroeconomic model. Multiple scenarios are considered that differ along two dimensions: (i) the coalition of countries (hubs) that initiate the decoupling, and (ii) whether non-hub countries are also forced to decouple via ‘preferential attachment’ – i.e. by aligning themselves with the hub they trade most with. All global technology hubs lose across scenarios, and losses are largest under preferential attachment. Smaller countries with relations that straddle multiple hubs generally lose, whereas those whose trade is heavily concentrated with one hub may gain due to reduced competition under some scenarios. Technological fragmentation can lead to losses in the order of 5 percent of GDP for many economies.

Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations to enjoy a log-normal citation distribution when it was found to have grown in accordance with preferential attachment? This anomalous result, which we exalt as the preferential attachment paradox, has remained unexplained since the physicist Sidney Redner first made light of it over a decade ago. Here we propose a resolution. The chief source of the mischief, we contend, lies in Redner having relied on a measurement procedure bereft of the accuracy required to distinguish preferential attachment from another form of attachment that is consistent with a log-normal in-degree distribution. There was a high-accuracy measurement procedure in use at the time, but it would have have been difficult to use it to shed light on the paradox, due to the presence of a systematic error inducing design flaw. In recent years the design flaw had been recognised and corrected. We show that the bringing of the newly corrected measurement procedure to bear on the data leads to a resolution of the paradox.

Homophily, Preferential Attachment or Triadic Closure? How the Topology of Acquaintance Networks is Determined by Processes of Link Creation

BackgroundMany biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.ResultsIn this paper, we focus on the robustness of a network that is acquired during its evolutionary process. Through simulations using Boolean network models, we found that preferential attachment increases the number of coupled feedback loops in the course of network evolution. Whereas, if networks evolve to have more coupled feedback loops rather than following preferential attachment, the resulting networks are more robust than those obtained through preferential attachment, although both of them have similar degree distributions.ConclusionThe presented analysis demonstrates that coupled feedback loops may play an important role in network evolution to acquire robustness. The result also provides a hint as to why various biological networks have evolved to contain a number of coupled feedback loops.

Local and global degree profiles of randomly grown self-similar hooking networks under uniform and preferential attachment

Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by the observation that the average degree growth of nodes is time invariant in empirical network data, we study the degree dynamics in the relevant class of network models where preferential attachment is combined with heterogeneous node fitness and aging. We propose an analytical framework based on the time invariance of the studied systems and show that it is self-consistent only for two special network growth forms: the uniform and the exponential network growth. Conversely, the breaking of such time invariance explains the winner-takes-all effect in some model settings, revealing the connection between the Bose-Einstein condensation in the Bianconi-Barabási model and similar gelation in superlinear preferential attachment. Aging is necessary to reproduce realistic node degree growth curves and can prevent the winner-takes-all effect under weak conditions. Our results are verified by extensive numerical simulations.

Spontaneous Reporting Systems [SRS] are critical tools in the post-licensure evaluation of medical product safety. Regulatory authorities use a variety of data mining techniques to detect potential safety signals in SRS databases. Assessing the performance of such signal detection procedures requires simulated SRS databases, but simulation strategies proposed to date each have limitations. We sought to develop a novel SRS simulation strategy based on plausible mechanisms for the growth of databases over time. We developed a simulation strategy based on the network principle of preferential attachment. We demonstrated how this strategy can be used to create simulations based on specific databases of interest, and provided an example of using such simulations to compare signal detection thresholds for a popular data mining algorithm. The preferential attachment simulations were generally structurally similar to our targeted SRS database, although they had fewer nodes of very high degree. The approach was able to generate signal-free SRS simulations, as well as mimicking specific known true signals. Explorations of different reporting thresholds for the FDA Vaccine Adverse Event Reporting System suggested that using proportional reporting ratio [PRR] > 3.0 may yield better signal detection operating characteristics than the more commonly used PRR > 2.0 threshold. The network analytic approach to SRS simulation based on the principle of preferential attachment provides an attractive framework for exploring the performance of safety signal detection algorithms. This approach is potentially more principled and versatile than existing simulation approaches. The utility of network-based SRS simulations needs to be further explored by evaluating other types of simulated signals with a broader range of data mining approaches, and comparing network-based simulations with other simulation strategies where applicable.

Sampling from large graphs is an area which is of great interest, particularly with the recent emergence of huge structures such as Online Social Networks. These often contain hundreds of millions of vertices and billions of edges. The large size of these networks makes it computationally expensive to obtain structural properties of the underlying graph by exhaustive search. If we can estimate these properties by taking small but representative samples from the network, then size is no longer a problem.In this paper we develop an analysis of random walks, a commonly used method of sampling from networks. We present a method of biassing the random walk to acquire a complete sample of high degree vertices of social networks, or similar graphs. The preferential attachment model is a common method to generate graphs with a power law degree sequence. For this model, we prove that this sampling method is successful with high probability. We also make experimental studies of the method on various real world networks.For t-vertex graphs G(t) generated by a preferential attachment process, we analyze a biassed random walk which makes transitions along undirected edges {x,y} proportional to [d(x)d(y)]b, where d(x) is the degree of vertex x and b > 0 is a constant parameter. Let S(a) be the set of all vertices of degree at least ta in G(t). We show that for some b approx 2/3, if the biassed random walk starts at an arbitrary vertex of S(a), then with high probability the set S(a) can be discovered completely in ~O(t1-(4/3)a+d) steps, where d is a very small positive constant. The notation ~O ignores poly-log t factors.The preferential attachment process generates graphs with power law 3, so the above example is a special case of this result. For graphs with degree sequence power law c>2 generated by a generalized preferential attachment process, a random walk with transitions along undirected edges {x,y} proportional to (d(x)d(y))(c-2)/2, discovers the set S(a) completely in ~O(t1-a(c-2)+d) steps with high probability. The cover time of the graph is ~O(t).Our results say that if we search preferential attachment graphs with a bias b=(c-2)/2 proportional to the power law c then, (i) we can find all high degree vertices quickly, and (ii) the time to discover all vertices is not much higher than in the case of a simple random walk. We conduct experimental tests on generated networks and real-world networks, which confirm these two properties.

Graphical virtual worlds add two new layers to the old question what determines friendship formation. First, it is possible to distinguish between off-line (player) and online (avatar) characteristics. Second, these environments offer new possibilities for studying friendship formation. By tracking friendship requests and their acceptance rate, researchers are able to distinguish between with whom players want to become friends and with whom they actually do become friends. This article examined friendship formation in Timik, a graphical virtual world targeted at Polish teenagers. Homophily, preferential attachment and status were tested as possible underlying mechanisms. Results showed that preferential attachment and status drove invitations: Players wanted to become friends with high-status players. However, high-status players were also more likely to reject offers. Homophily only played a minor role. Players preferred players of the same avatar class and similar age but of the opposite sex. Too similar avatars were disliked. The results are discussed in the light of the generalizability of off-line theories of friendship formation to online worlds.