A Weighted Statistical Network Modeling Approach to Product Competition Analysis

Statistical network models have been used to study the competition among different products and how product attributes influence customer decisions. However, in existing research using network-based approaches, product competition has been viewed as binary (i.e., whether a relationship exists or not), while in reality, the competition strength may vary among products. In this paper, we model the strength of the product competition by employing a statistical network model, with an emphasis on how product attributes affect which products are considered together and which products are ultimately purchased by customers. We first demonstrate how customers’ considerations and choices can be aggregated as weighted networks. Then, we propose a weighted network modeling approach by extending the valued exponential random graph model to investigate the effects of product features and network structures on product competition relations. The approach that consists of model construction, interpretation, and validation is presented in a step-by-step procedure. Our findings suggest that the weighted network model outperforms commonly used binary network baselines in predicting product competition as well as market share. Also, traditionally when using binary network models to study product competitions and depending on the cutoff values chosen to binarize a network, the resulting estimated customer preferences can be inconsistent. Such inconsistency in interpreting customer preferences is a downside of binary network models but can be well addressed by the proposed weighted network model. Lastly, this paper is the first attempt to study customers’ purchase preferences (i.e., aggregated choice decisions) and car competition (i.e., customers’ co-consideration decisions) together using weighted directed networks.

Applied Research on the Combination of Weighted Network and Supervised Learning in Acupoints Compatibility

To enhance the depth of excavation and promote the intelligence of acupoint compatibility, a method of constructing weighted network, which combines the attributes of acupoints and supervised learning, is proposed for link prediction. Medical cases of cervical spondylosis with acupuncture treatment are standardized, and a weighted network is constructed according to acupoint attributes. Multiple similarity features are extracted from the network and input into a supervised learning model for prediction. And, the performance of the algorithm is evaluated through evaluation indicators. The experiment finally screened 67 eligible medical cases, and the network model involved 141 acupoint nodes with 1048 edge. Except for the Preferential Attachment similarity index and the Decision Tree model, all other similarity indexes performed well in the model, among which the combination of PI index and Multilayer Perception model had the best prediction effect with an AUC value of 0.9351, confirming the feasibility of weighted networks combined with supervised learning for link prediction, also as a strong support for clinical point selection.

A weighted network analysis framework for the hourglass effect—And its application in the C. elegans connectome

Understanding hierarchy and modularity in natural as well as technological networks is of utmost importance. A major aspect of such analysis involves identifying the nodes that are crucial to the overall processing structure of the network. More recently, the approach of hourglass analysis has been developed for the purpose of quantitatively analyzing whether only a few intermediate nodes mediate the information processing between a large number of inputs and outputs of a network. We develop a new framework for hourglass analysis that takes network weights into account while identifying the core nodes and the extent of hourglass effect in a given weighted network. We use this framework to study the structural connectome of the C. elegans and identify intermediate neurons that form the core of sensori-motor pathways in the organism. Our results show that the neurons forming the core of the connectome show significant differences across the male and hermaphrodite sexes, with most core nodes in the male concentrated in sex-organs while they are located in the head for the hermaphrodite. Our work demonstrates that taking weights into account for network analysis framework leads to emergence of different network patterns in terms of identification of core nodes and hourglass structure in the network, which otherwise would be missed by unweighted approaches.

Hogyan befolyásolja a villamosenergia-hálózatról rendelkezésre álló információ a fizikai támadások által okozott sérülékenységről alkotott képet?

Összefoglaló. A villamosenergia-rendszerek fizikai támadásokkal szembeni ellenálló képessége a közelmúltban világszerte történt események ismeretében egyre nagyobb hangsúlyt kap a tématerület kutatásaiban. Az ilyen eseményekre való megfelelő felkészüléshez elengedhetetlen az üzemeltetett infrastruktúrának, elsősorban annak gyengeségeinek pontos ismerete. A cikkben Magyarország villamosenergia-hálózatának adatai alapján készített súlyozatlan és súlyozott gráfokon végzünk vizsgálatokat, hogy megértsük a különböző stratégia mentén kiválasztott célpontok elleni támadások milyen mértékben csökkentik a topológiai hatékonyságot. A cikk célja egyben a magyar hálózat sérülékenységének általános bemutatása is, mely hasznos bemeneti információ lehet a kockázati tervek elkészítésekor. Summary. Tolerance of the power grid against physical intrusions has gained importance in the light of various attacks that have taken place around the world. To adequately prepare for such events, grid operators have to possess a deep understanding of their infrastructure, more specifically, of its weaknesses. A graph representation of the Hungarian power grid was created in a way that the vertices are generators, transformers, and substations and the edges are high-voltage transmission lines. All transmission and sub-transmission elements were considered, including the 132 kV network as well. The network is subjected to various types of single and double element attacks, objects of which are selected according to different aspects. The vulnerability of the network is measured as a relative drop in efficiency when a vertex or an edge is removed from the network. Efficiency is a measure of the network’s performance, assuming that the efficiency for transmitting electricity between vertices i and j is proportional to the reciprocal of their distance. In this paper, simultaneous removals were considered, arranged into two scenarios (single or double element removal) and a total of 5 cases were carried out (single vertex removal, single edge removal, double vertex removal, double edge removal, single vertex and single edge removal). During the examinations, all possible removal combinations were simulated, thus the 5 cases represent 385, 504, 73920, 128271 and 193797 runs, respectively. After all runs were performed, damage values were determined for random and targeted attacks, and attacks causing maximal damage were also identified. In all cases, damage was calculated for unweighted and weighted networks as well, to enable the comparison of those two models. The aims of this paper are threefold: to perform a general assessment on the vulnerability of the Hungarian power grid against random and targeted attacks; to compare the damage caused by different attack strategies; and to highlight the differences between using unweighted and weighted graphs representations. Random removal of a single vertex or a single edge caused 0.3–0.4% drop in efficiency, respectively, which indicates a high tolerance against such attacks. Damage for random double attacks was still only in the range of 0.6–0.8%, which is acceptable. It was shown that if targets are selected by the attacker based on the betweenness rank of the element, damage would be below the maximal possible values. Comparison of the damage measured in the unweighted and the weighted network representations has shown that damage to the weighted network tends to be bigger for vertex attacks, but the contrary is observed for edge attacks. Numerical differences between the two representations do not show any trend that could be generalised, but in the case of the most vulnerable elements significant differences were found in damage measures, which underlines the importance of using weighted models.

Protection Strategy against an Epidemic Disease on Edge-Weighted Graphs Applied to a COVID-19 Case

Among the diverse and important applications that networks currently have is the modeling of infectious diseases. Immunization, or the process of protecting nodes in the network, plays a key role in stopping diseases from spreading. Hence the importance of having tools or strategies that allow the solving of this challenge. In this paper, we evaluate the effectiveness of the DIL-Wα ranking in immunizing nodes in an edge-weighted network with 3866 nodes and 6,841,470 edges. The network is obtained from a real database and the spread of COVID-19 was modeled with the classic SIR model. We apply the protection to the network, according to the importance ranking list produced by DIL-Wα, considering different protection budgets. Furthermore, we consider three different values for α; in this way, we compare how the protection performs according to the value of α.