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A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if every two of them are pairwisely edge-disjoint, they are called completely edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many network functionalities, and constructing CEISTs as maximally allowed as possible in a given network is a worthy undertaking. In this paper, we establish the maximal number of CEISTs in the locally twisted cube network, and propose an algorithm to construct $\lfloor \frac{n}{2} \rfloor$ CEISTs in $LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has been actually implemented, and we present the outputs. Network broadcasting in the $LTQ_n$ was simulated using $\lfloor\frac{n}{2}\rfloor$ CEISTs, and the performance compared with broadcasting using a single tree.

Competitive Influence Maximization (CIM) has been studied for years due to its wide application in many domains. Most current studies primarily focus on the micro-level optimization by designing policies for one competitor to defeat its opponents. Furthermore, current studies ignore the fact that many influential nodes have their own starting prices, which may lead to inefficient budget allocation. In this paper, we propose a novel Competitive Bidding Influence Maximization (CBIM) problem, where the competitors allocate budgets to bid for the seeds attributed to the platform during multiple bidding rounds. To solve the CBIM problem, we propose a Fairness-aware Multi-agent Competitive Bidding Influence Maximization (FMCBIM) framework. In this framework, we present a Multi-agent Bidding Particle Environment (MBE) to model the competitors' interactions, and design a starting price adjustment mechanism to model the dynamic bidding environment. Moreover, we put forward a novel Multi-agent Competitive Bidding Influence Maximization (MCBIM) algorithm to optimize competitors' bidding policies. Extensive experiments on five datasets show that our work has good efficiency and effectiveness., Comment: IEEE Transactions on Computational Social Systems (TCSS), 2023, early access

Network representation learning (NRL) advances the conventional graph mining of social networks, knowledge graphs, and complex biomedical and physics information networks. Over dozens of network representation learning algorithms have been reported in the literature. Most of them focus on learning node embeddings for homogeneous networks, but they differ in the specific encoding schemes and specific types of node semantics captured and used for learning node embedding. This survey paper reviews the design principles and the different node embedding techniques for network representation learning over homogeneous networks. To facilitate the comparison of different node embedding algorithms, we introduce a unified reference framework to divide and generalize the node embedding learning process on a given network into preprocessing steps, node feature extraction steps and node embedding model training for a NRL task such as link prediction and node clustering. With this unifying reference framework, we highlight the representative methods, models, and techniques used at different stages of the node embedding model learning process. This survey not only helps researchers and practitioners to gain an in-depth understanding of different network representation learning techniques but also provides practical guidelines for designing and developing the next generation of network representation learning algorithms and systems.

Graph embedding is a powerful method in parallel computing that maps a guest network $G$ into a host network $H$. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the wirelength. In this manuscript, we obtain the wirelength (exact and minimum) of embedding complete multi-partite graphs into Cartesian product of paths and cycles, which include $n$-cube, $n$-dimensional mesh (grid), $n$-dimensional cylinder and $n$-dimensional torus, etc., as the subfamilies., Comment: 16 Pages, 5 figures

DCell has been proposed for data centers as a server centric interconnection network structure. DCell can support millions of servers with high network capacity by only using commodity switches. With one exception, we prove that a $k$ level DCell built with $n$ port switches is Hamiltonian-connected for $k \geq 0$ and $n \geq 2$. Our proof extends to all generalized DCell connection rules for $n\ge 3$. Then, we propose an $O(t_k)$ algorithm for finding a Hamiltonian path in $DCell_{k}$, where $t_k$ is the number of servers in $DCell_{k}$. What's more, we prove that $DCell_{k}$ is $(n+k-4)$-fault Hamiltonian-connected and $(n+k-3)$-fault Hamiltonian. In addition, we show that a partial DCell is Hamiltonian connected if it conforms to a few practical restrictions., Comment: To appear