Blockchain nodes communicate over a peer-to-peer (P2P) network, with researchers exploring decentralization properties.Network topology is crucial in terms of clustering properties and maintaining safety and liveness.Ledger systems must maintain connections to avoid eclipse attacks and ensure network partition tolerance.An attacker can compromise safety and privacy by isolating nodes in the network and controlling communications.Bootstrapping nodes need to connect to honest peers to avoid compromising system properties and privacy.Connecting to honest peers poses challenges due to the lack of knowledge about network participants.Catching up from genesis may not always be feasible, leading to potential safety violations in PoS systems.Maintaining network privacy and ensuring liveness are ongoing challenges in decentralized ledger systems.Some proposals aim to enhance privacy and security using computational assumptions rather than trusted setups.