Fuzzy Clustering in Assortative and Disassortative Networks

Despite the significance of assortativity as a property of networks that paves for the emergence of new structural types, surprisingly, there has been little research done on assortativity. Assortative networks are perhaps among the most prominent examples of complex networks believed to be governed by common phenomena, thereby producing structures far from random. Further, certain vertices possess high centrality and can be regarded as significant and influential vertices that can become cluster centers that connect with high membership to many of the surrounding vertices. We propose a fuzzy clustering method to meaningfully characterize assortative, as well as disassortative, networks by adapting the Bonacichi’s power centrality to seek the high degree centrality vertices to become cluster centers. Moreover, we leverage our novel modularity function to determine the optimal number of clusters, as well as the optimal membership among clusters. However, due to the difficulty of finding real-world assortative network datasets that come with ground truths, we evaluated our method using synthetic data but possibly bearing resemblance to real-world network datasets as they were generated by the Lancichinetti–Fortunato–Radicchi benchmark. Our results show our non-hierarchical method outperforms a known hierarchical fuzzy clustering method, and also performs better than a well-known membership-based modularity function. Our method proved to perform beyond satisfactory for both assortative and disassortative networks.

Complex interaction networks of cytokines after transarterial chemotherapy in patients with hepatocellular carcinoma

Inflammation in the tumor microenvironment influences all stages of HCC development and progression as well as the anti-cancer response by immune system. In this study, we studied cytokine networks before and after transarterial chemotherapy (TACE). Serum samples obtained from 203 HCC patients treated with TACE were analyzed for inflammatory cytokines including interleukin (IL)-1β, IL-2, IL-4, IL-5, IL-6, IL-9, IL-10, IL-12, IL-13, IL-17, IL-22, TNF-α, IFN-γ, and C-reactive protein (CRP) levels. Cytokine concentrations were measured at day 0 (D0, baseline), day3 (D3), day7 (D7), and day 60 (D60) after TACE. Network analysis revealed that modules within cytokine network at D0 were lost by D60 and modularity value (Mc) was decreased from 0.177 at D0 to −0.091 at D60. D60 had the lowest network heterogeneity and lower diameter, clustering coefficient, network density and recruited nodes. Degree correlation revealed that assortative network turned to disassortative network by D60 indicating that the network gained scale free feature. CRP, IL-2 were components of modules related with adverse outcome and IL-13, favorable outcome. Median survival month of patient group with high and low values with P-values were as follows: D0 CRP, 9.5 month (M), 54.2M (P<0.0001); D0 IL-2, 39.9M, 56.1M (P=0.0084); D3 CRP, 31.3M, 55.1 M (P=0.0056); D7 CRP, 28.7M, 50.7M (P=0.0065); IL-13, 51.9M, 33.6M (P=0.06). Network modularity decreased with temporal changes. Components of modules that included CRP, IL-2 and IL-6 were associated with adverse outcome and short overall survival. These modules were dissolved by D60 after TACE. Degree correlation decreased by D60, indicating that the cytokine network gained the scale free network property as in other biological network. TACE treatment converted cytokine network from that with inflammatory module to that with scale free network feature and without modules. Further studies are required to verify temporal changes of cytokine network in HCC patients after TACE.

Second-order centrality correlation in scale-free networks

Scale-free networks in which the degree displays a power-law distribution can be classified into assortative, disassortative, and neutral networks according to their degree–degree correlation. The second-order centrality proposed in a distributed computation manner is quick-calculated and accurate to identify critical nodes. We explore the second-order centrality correlation (SOC) for each type of the scale-free networks. The SOC–SOC correlation in assortative network and neutral network behaves similarly to the degree–degree correlation, while it behaves an apparent difference in disassortative networks. Experiments show that the invulnerability of most of scale-free networks behaves similarly under the node removal ordering by SOC centrality and degree centrality, respectively. The netscience network and the Yeast network behave a little differently because they are native disconnecting networks.

The Analysis of the Properties of Bus Network Topology in Beijing Basing on Complex Networks

The transport network structure plays a crucial role in transport dynamics. To better understand the property of the bus network in big city and reasonably configure the bus lines and transfers, this paper seeks to take the bus network of Beijing as an example and mainly use space L and space P to analyze the network topology properties. The approach is applied to all the bus lines in Beijing which includes 722 lines and 5421 bus station. In the first phase of the approach, space L is used. The results show that the bus network of Beijing is a scale-free network and the degree of more than 99 percent of nodes is lower than 10. The results also show that the network is an assortative network with 46 communities. In a second phase, space P is used to analyze the property of transfer. The results show that the average transfer time of Beijing bus network which is 1.88 and 99.8 percent of arbitrary two pair nodes is reachable within 4 transfers.

DEGREE AND WEIGHTED PROPERTIES OF THE DIRECTED CHINA RAILWAY NETWORK

As well known, many real complex systems are directed and weighted ones. For understanding the topology structure of the directed China Railway Network (CRN) further, we analyze the degree properties of the directed CRN and propose a new method to measure the weight of station (i.e., the utilized efficiency of station) in CRN according to how CRN works really. Rigorous analysis of the existing CRN data shows that the CRN is an assortative network with scale-free degree distribution in space L. On the other hand, the cumulative distribution of station's relative weight, the cumulative distribution of the shortest path length between stations, and the relationship between relative weight and in-(out-)degree have been studied. Our present work provides a new perspective to define the weight of transport complex network, which will be helpful for studying the dynamics of CRN.

GENERATING AN ASSORTATIVE NETWORK WITH A GIVEN DEGREE DISTRIBUTION

Recently, the assortative mixing of complex networks has received much attention partly because of its significance in various social networks. In this paper, a new scheme to generate an assortative growth network with given degree distribution is presented using a Monte Carlo sampling method. Since the degrees of a great number of real-life networks obey either power-law or Poisson distribution, we employ these two distributions to grow our models. The models generated by this method exhibit interesting characteristics such as high average path length, high clustering coefficient and strong rich-club effects.