Graph theory has become a very critical component in many applications in the computing field including networking and security. Unfortunately, it is also amongst the most complex topics to understand and apply. In this paper, we review some of the key applications of graph theory in network security. We first cover some algorithmic aspects, then present network coding and its relation to routing.

We consider the problem of establishing reliable unicast connections in the presence of edge failures. In this problem, a source node s needs to deliver h packets to the destination node t, even if one of the edges in the network fails. We apply the the technique of network coding in order to guarantee an instantaneous recovery from edge failures. Focusing on the case of h = 2, we show that the...

Network coding is known as a promising approach to improve wireless network performance. How to discover the coding opportunity in relay nodes is really important for it. There are more coding chances, there are more times it can improve network throughput by network coding operation. In this paper, an extended network coding opportunity discovery scheme (ExCODE) is proposed, which is realized ...

We compare multicast network coding and routing for a time-varying wireless network model with interferencedetermined link capacities. We use dynamic back pressure algorithms that are optimal for intra-session network coding and routing respectively. Our results suggest that under such conditions, the gap in multicast capacity between network coding and routing can decrease relative to a collis...

In this paper, we, based on NS-2 simulator, evaluate the performances of different TCP protocols with network coding in wireless multihop networks, and then propose two schemes to enhance the performances of TCPs with network coding. In particular the network coding scheme considered and used here is COPE, which is one of the well-known practical network coding schemes, the TCP protocols evalua...

Our primary goal in this paper is to traverse the performance gap between two linear network coding schemes: random linear network coding (RLNC) and instantly decodable network coding (IDNC) in terms of throughput and decoding delay. We first redefine the concept of packet generation and use it to partition a block of partially-received data packets in a novel way, based on the coding sets in a...

A directed acyclic network is considered where all the terminals demand the sum of the symbols generatedat all the sources. We call such a network as a sum-network. It is shown that there exists a solvably (and linearsolvably) equivalent sum-network for any multiple-unicast network (and more generally, for any acyclic directednetwork where each terminal node demands a subset of ...

The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer to test whether a certain rate vector is achievable with vector linear network codes for a multisource network coding instance and whether there exists a mul...