Honest cluster

1. Attack edges Honest peers Sybil peers Honest cluster Sybil cluster

3. v v.fingers

4. u2 (s,t)-rw moves from v to u v u s u3 (s,t)-rw moves from u to v t e=(v,u) An example of the variable in RWBC. $(s,t)$-rw denotes a $(s,t)$ random walk, represented by the dot dash line. The real lines represent the edges between peers. $e.i_v^{(s,t)}$: expected number of times that a (s,t) random walk passing e from $v$ to $u$ Partical betweenness of e: $|e.i_v^{(s,t)}-e.i_u^{(s,t)}|$ Betweenness of e: $$ Betweenness of v: $$

5. u2 (s,t)-RWs move from v to u C (s,t) random walks v u s (s,t)-RWs move from u to v e=(v,u) t

6. v m u s t e=(v,u) m m1={s:i,t:j, …} v u i j m2={s:i,t:j,…}

7. ae1 s rw ae2 t ae3 Honest peers Sybil peers An example showing that the number of times that a second type steered random walk traverses the attack edges is an odd number. Dot dash line is a second type $(s,t)$ random walk, denoted by $rw$. $ae1$, $ae2$ and $ae3$ are three attack edges. Then, the number of times that $rw$ traverses the attack edges must be an odd number (3, in this example)

8. a a C1 C2 C1 C2 b b c c