Knowledge bases of entities and relations (either constructed manually or automatically) are behind many real world search engines, including those at Yahoo!, Microsoft, and Google. Those knowledge bases can be viewed as graphs with nodes representin
g entities and edges representing (primary) relationships, and various studies have been conducted on how to leverage them to answer entity seeking queries. Meanwhile, in a complementary direction, analyses over the query logs have enabled researchers to identify entity pairs that are statistically correlated. Such entity relationships are then presented to search users through the related searches feature in modern search engines. However, entity relationships thus discovered can often be puzzling to the users because why the entities are connected is often indescribable. In this paper, we propose a novel problem called entity relationship explanation, which seeks to explain why a pair of entities are connected, and solve this challenging problem by integrating the above two complementary approaches, i.e., we leverage the knowledge base to explain the connections discovered between entity pairs. More specifically, we present REX, a system that takes a pair of entities in a given knowledge base as input and efficiently identifies a ranked list of relationship explanations. We formally define relationship explanations and analyze their desirable properties. Furthermore, we design and implement algorithms to efficiently enumerate and rank all relationship explanations based on multiple measures of interestingness. We perform extensive experiments over real web-scale data gathered from DBpedia and a commercial search engine, demonstrating the efficiency and scalability of REX. We also perform user studies to corroborate the effectiveness of explanations generated by REX.
Many real systems possess accelerating statistics where the total number of edges grows faster than the network size. In this paper, we propose a simple weighted network model with accelerating growth. We derive analytical expressions for the evoluti
ons and distributions for strength, degree, and weight, which are relevant to accelerating growth. We also find that accelerating growth determines the clustering coefficient of the networks. Interestingly, the distributions for strength, degree, and weight display a transition from scale-free to exponential form when the parameter with respect to accelerating growth increases from a small to large value. All the theoretical predictions are successfully contrasted with extensive numerical simulations.
The exact formula for the average path length of Apollonian networks is found. With the help of recursion relations derived from the self-similar structure, we obtain the exact solution of average path length, $bar{d}_t$, for Apollonian networks. In
contrast to the well-known numerical result $bar{d}_t propto (ln N_t)^{3/4}$ [Phys. Rev. Lett. textbf{94}, 018702 (2005)], our rigorous solution shows that the average path length grows logarithmically as $bar{d}_t propto ln N_t$ in the infinite limit of network size $N_t$. The extensive numerical calculations completely agree with our closed-form solution.
We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the networks follo
w a power-law degree distribution, with degree exponent continuously tuned between 2 and 3. The exact expression of clustering coefficient is also provided for the networks. Furthermore, the investigation of the average path length reveals that the networks possess small-world feature. Interestingly, we find that a special case of our model can be mapped into the Yule process.
We propose a synthetical weights dynamic mechanism for weighted networks which takes into account the influences of strengths of nodes, weights of links and incoming new vertices. Strength/Weight preferential strategies are used in these weights dyna
mic mechanisms, which depict the evolving strategies of many real-world networks. We give insight analysis to the synthetical weights dynamic mechanism and study how individual weights dynamic strategies interact and cooperate with each other in the networks evolving process. Power-law distributions of strength, degree and weight, nontrivial strength-degree correlation, clustering coefficients and assortativeness are found in the model with tunable parameters representing each model. Several homogenous functionalities of these independent weights dynamic strategy are generalized and their synergy are studied.
Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks,
which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indi
cate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems.
